Dolomites Weather in Mid May?

It is impossible to predict weather 3 months in advance. All you can have is historical averages.
For example in Ortisei (Val Gardena) or Cortina the average minimum temperature in May is 4 degrees centigrade (40F) while the average max temp in the early afternoon is 15 C (59 F). Precipitation in May is likely, but whether it's snow or rain depends on the temperature. In May snow is certainly possible at high elevations but usually unlikely below 2000 mt ASL. (~ 7000 ft). Ortisei or Cortina are both at 1200 mt above sea level (4000 ft) and temperatures drop 1 degree Celsius for every 100 mt in altitude on a sunny day and drop 0.6 degree C for every 100mt on a rainy/cloudy day.

As Roberto said, especially in mountain areas, the weather is difficult to predict, even a couple of days in advance, let alone weeks or months before.
Mountain weather, for technical meteorological reasons, is especially difficult to predict. Sometimes you have to wait until you get there to know what the weather will be.
You just have to take what the weather gods see fit to grant you. Makes it hard to make advance plans.

As Kent and Roberto have said, you never know. We go to the area (specifically Ortisei) somewhat frequently. Last December -- on Christmas Day in fact -- there was little snow and we hiked in the high meadow under sunny skies and 40-45 degrees F. We've been there in July when it was barely 40 degrees in the same spot but it warmed to 60. We've had thunderstorms in the AM and beautiful clear weather by Noon. The key is, to me, to spend enough days that you enhance your chances of getting good weather. (The same philosophy holds in the Jungfrau Region in Switzerland.)
If you only spend two nights and your ONE DAY is cold and rainy, well it won't be great. But if you can spend 4 nights and THREE days, chances are you will get some good weather and it might ALL be good.

We were there around that time and, yes, it's too early but we still enjoyed it. Lots of places were closed - including the cable cars - and there was a lifeless feeling. However the valley floor was green up to about 1000 feet above the valley bottom, and it wasn't cold. We found a nice hike and got tired enough to be satisfied.

I don't think you will want to spend that long in the mountains, though. Trento is nice as is Merano and at Bolzano you can say hi to my BFF, the amazing Iceman, Otzi.