As 36 year resident of Colorado's high country and a 30 year resident of Estes Park, I can tell you May can be a tough travel month. In Rocky, Trail Ridge Road in all likely hood will not be open. Traditional opening date is Memorial Day weekend. Can be a little earlier in a drought year.
You did not mention what your activity expectations are. Bear Lake will have some leftover snow. Lakes above will probably be frozen or partially frozen. Trails will be icy in the morning and slushy in the afternoon. Or you can have a really warm May with many trails more accessible. If you are only a car tourist interested in scenery, May is ok. You will miss the summer crowds in places like Estes Park and Aspen.
I remember a mid May storm in Estes Park that dumped almost 3' of snow with temps in the teens. I also remember a Memorial Day weekend storm with a couple feet of wet snow that shut down most roads. We called those storms "May dumps" then again it may not dump! I remember many beautiful warm and dry Mays. Snow storms that shut passes are not uncommon into early June.
The bottom line is that May can be very unsettled. Bring shorts, heavy coats and everything in between. The good news at the storms are usually quick hitters with the snow melting in 24-48 hours. Just stay informed and be prepared to hang out.