score:7
I was in the Dolomites late April / early May 2003.
In the lower valleys, it's essentially summer. Places like Bozen/Bolzano can be well over 20°C and reaching 30°C. If you're fine hiking in the valleys, you'll have no problem at all.
Higher land will be covered in snow. You won't be able to hike there. Where the snow starts varies on the slope and the season. You might find patches of snow below 1600 metre, or you might find that you can hike well above 2000 metre. 2003 had an extremely warm spring, so snow was mostly gone.
You should not expect any fresh snowfall in May.
In summary, May is a good time to hike in the Dolomites, just don't expect you can do the hikes you would do in summer. Details will vary from year to year.