Did medieval Europeans really walk around barefoot in winter?

The "especially in winter" part is most certainly an exaggeration, but for a lot of regions not completely impossible:

When being well-fed, used to it, with thick scale-like skin developing, otherwise healthy and moving, one can run around for quite a bit longer barefooted in lightly freezing temperatures than popularly expected. The body temperature delivered via the circulatory system being the critical variable. In Northern Finland such a time-frame will of course be much shorter than in medieval Spain near the coast. But very few will catch frostbite immediately when touching snow or ice. (Description of an enthusiast, or two.)

Then, not all regions and times really had always temperatures much below zero degrees Celsius when it was winter. In fact the medieval warm period would suggest that it may have been quite a bit milder into higher latitudes then we would expect by looking at Dutch masters depicting a very frosty environment for the same regions in their time.

That is not saying that the European climate was that much milder either. That Northern Europeans would always walk around barefooted even near the Polar circle is surely either an overstatement or a wild inaccuracy neglecting the northerly and more easterly parts of 'Europe'. Continental European climates were even back then too uninviting for 'never wearing shoes' in winter. Physical hardiness has its limits.

Within these parameters a lot of people indeed went about barefooted a lot of the time, just not always in winter:

Why go barefoot if simple shoes of cured skin were available? People appear to have gone without shoes though the protection and warmth provided to the feet by these simple shoes in our colder northern climates would have been welcome inferring that they were no longer commonly used. Medieval illustrations show members of the least favoured sectors of society, such as beggars, lepers and the sick, barefoot. We may presume that a significant percentage of another part of the population, namely the children, frequently went barefoot as they did throughout much of our history, indeed, many photographs taken at the turn of the 20th century show children of the English working classes barefoot. The proportion of the wider medieval population who went barefoot is difficult to judge however. The Luttrell Psalter written and illuminated in England during the second quarter of the 14th century provides a wonderful picture of rural life at that time. Most of the country folk shown going about their everyday activities are in shoes or footed hose, but occasionally certain jobs such as the threshing of corn are depicted being undertaken barefoot.
_{— Gitte Hansen, Steven P. Ashby & Irene Baug (Eds) : "Everyday products in the Middle Ages: crafts, consumption and the individual in northern Europe, c. AD 800–1600", Oxbow Books: Oxford, Havertown, 2015.}

But notice the seasons mentioned here. My grandma made quite the point of me sickly child not going around enough without shoes, as that would make me weak and even sick. But even she had to admit that in winter, not having freezing feet was a priority for her. And as an intermediate experiment to maybe indulge in, wear Roman-style sandals when it's freezing without any socks and then walk around really barefoot when it's below zero. As long as it's not snowy-wet, that is doable for quite a while. But don't stand or sit or even sleep, which is a recipe for quite a quick problem…

These aspects of parsimony and hardiness come together in most accounts of barefoot in winter, like in an adventus nudis pedibus for for example a bishop coming into a city, the so-called 'episcopal entry':

Norbert must have been well known for such humble behavior, rather popular among the contemporary ecclesiastical reformists. During the strong winter 1118/1119 he preached in southern France while wandering barefoot around the country. In the same period, we hear about two barefooted episcopal entries.
_{— Jacek Maciejewski: "Nudo Pede Intrat Urbem: Research on The Adventus of a Medieval Bishop through the First Half of the Twelfth Century", Viator 41 No. 1 (2010) 89–100. 10.1484/J.Viator.1.100568.}

Here with added gravitas, as usually bishops would ride on a horse while wearing shoes themselves, then dismount and only make the final approach in that manner.

Going barefoot, particularly mid-winter, was a public demonstration of hardiness. The Reverend John Eldar from the Western Isles of Scotland wrote a letter to King Henry VIII in 1544 in which he boasts of this barefoot fashion among the Islanders. He wrote:

We of all and best people can tolerat, suffir, and away best with colde, for boithe somer and wyntir (excepte whene the froest is mooste vehemente), goynge always bair and bair leggide footide, our delite and pleasure is not onely in hwntynge of redd deir, wolfes, foxes, and graies, wherof we abounde, and haue greate plentie but also in rynninge, leapinge, swymmynge, shootynge, and of thrawinge dartis: therefor, in so moche as we vse and delite so to go alwaies the tendir delicatt gentillmen of Scotland, call ws Reddshankes.

Since the Reverend Eldar hastens to add that Redshanks dress like any other courtier when visiting the king in Edinburgh we are again dealing with a macho fashion a deliberate choice rather than poverty or ignorance. The bare feet and bare legs in the late sixteenth-century portrait of Captain Thomas Lee, the English commanding officer of Queen Elizabeth's regiment of Irish kerne, was not only a whimsical effort on his part to devise a dress uniform for his regiment, while pandering to the French and English fashion in the last years of the sixteenth century for men to show off the full length of their shapely legs, but also demonstrate that he had bought into Irish ideas of hardiness and heroism. He had married an Irish wife…
_{— Katharine Simms: "The Barefoot Kings: Literary Image and Reality in Later Medieval Ireland", Proceedings of the Harvard Celtic Colloquium, Vol. 30 (2010), pp1–21.}

The final advice on this is of course older than dirt:

The association of winter with warm clothing is made very early on inliterature. Hesiod (Works and Days) advises his readers to dress well in the month of Lenacon (the 1st part of January and the first part February):

"Then put on, as I bid you,[…] Lace on your feet close-fitting boots of the hide of a slaughtered ox, thickly lined with felt inside.…

_{— Carol E. Steer: "The Season Of Winter In Art And Literature From Roman North Africa To Medevieal France", Master Thesis, University Of Manitoba, 2000.}