Did the poor performance of the Red Army in the Winter War significantly contribute to German underestimation of the USSR's military capacity?

Absolutely. What other conclusion could you draw from that war?

Moreover, it was not an underestimation at all. The assessment was absolutely correct. When Germany attacked in June of 1941 the USSR was crushed, losing huge numbers of troops and territory. During that first summer the Soviet forces exhibited all the same obsolete equipment and incompetent strategy that had lost them the Winter War.

What the Germans underestimated was the ability of the Soviets to improve their army, their determination to fight and their ability to find new technological and military resources to resist.

However one should never forget that conditions in Finnish-Russo Winter War were hard, fighting was fierce, both Finns and Russians took quite a few POW's and partly the "poor level of Red Army" was a myth.

Think about this one: 30 times more Soviet soldiers died than was captured. 40 times more Finns were killed than captured.

Finnish-Winter War was just like battle in Rhzev meat grinder (1942-43) a battle scene those surviving front line soldiers remembered with special horror.

As a Finn i have several times wondered how successful western allies (or Germans) have been there in cold horror battlefields in Finland. Later Finns noticed how poorly many Germans were fighting in similar conditions. That's the "poor Red Army" during Winter War is partly a myth. They fought better than generally have believed.

Albert Speer speaking in the 1973 documentary The World at War: "Barbarossa (June – December 1941)"

"In August 39, when Hitler had signed the pact with Russia, in the evening there was a movie, and this movie showed the parade of the Russian troops before the Kremlin. He was very much impressed and was relived that now with the pact this army is neutralised. But afterwards when the German troops met the Russian ones in occupied Poland, officers reported to Hitler said the equipment of those Russian units were very poor. He first didn't believe it so much but then when the Russians attacked the Finns and they didn't have any progress he was convinced that this was really the truth and he was now considering the Russian army no more as strong as before."

So it would seem the questioner assertion is justified, the Winter War was important to changing Hitler's view of the Russian Army. I believe this source carries a lot of weight due to Speer's familiarity with Hitler. Also, the contention some historians have with Speers seems mostly to be over the extent to which he was aware or involved with the regime's atrocities, which I don't see being relevant here.

This is my own transcript. He's speaking at about 5:30 into the documentary. I'm sure it's available online, but I'm also sure I can't link that sort of thing.

Antony Beevor's Stalingrad contains some supporting material on perceived weaknesses of the Red Army esp. following Stalin's domestic purges:

Such confidence [in the success of Operation Barbarossa] was, in many ways, understandable. Every foreign intelligence service expected the Red Army to collapse. The Wehrmacht had assembled the largest invasion force ever seen [...]

Hitler's conviction that the Soviet Union was a 'rotten structure' that would come 'crashing down' was shared by many foreign observers and intelligence services. Stalin's purge of the Red Army, which had begun in 1937, was fueled by an inimitable mixture of paranoia, sadistic megalomania and a vindictiveness for old slights dating back to the Russian civil war and the Russo-Polish war.

Altogether, 36,671 officers were executed, imprisoned or dismissed, and out of the 706 officers of the rank of brigade commander and above, only 303 remained untouched [...]

The most prominent victim was Marshal Mikhail Tukhachevsky, the leading advocate of mobile warfare. His arrest and execution also represented the deliberate destruction of the Red Army's operational thinking, which had encroached dangerously upon Stalin's preserve of strategy [...]

Two and a half years after the purge began, the Red Army presented a disastrous spectacle in the Winter War against Finland. Marshal Voroshilov, Stalin's old crony from the 1st Cavalry Army, displayed an astonishing lack of imagination. The Finns outmaneuvered their opponents time after time. Their machine gunners scythed down the massed Soviet infantry struggling forward through the snowfields. Only after deploying five times as many men as their opponents, and huge concentrations of artillery, did the Red Army begin to prevail. Hitler had observed this lamentable performance with excitement.

Japanese military intelligence took rather a different view. It was about the only foreign service which did not underestimate the Red Army at this time. A series of border skirmishes on the Manchurian frontier, which culminated in the battle at Khalkin-Gol in August 1939, had shown what an aggressive young commander, in this case the forty-three -old General Georgy Zhukov, could achieve.

As for the key sentence ("Hitler had observed ...") Beevor does not point to further sources, so you would have to believe his word as an expert that he certainly is.