You can expect the weather to be cold and chilly. There's always a chance that the weather will be nice, but spring/early summer doesn't usually arrive until May/June, which is my favorite time to travel around the county. A couple of years ago we were camping at Dog Lake - Temperatures for the first day of summer reached freezing and there had been snow just before we arrived, it was COLD setting up camp. It has been known to snow/freeze on the 4th of July at times. So, be prepared for the cooler temperatures and alot of wind no matter what time of year.
I enjoy going during late May or June because things are green and the wildflowers are in bloom. After July 4, the weather usually heats up in a hurry and the landscape turns brown quickly - usually by the end of the month. In the later summer season, the high altitude lakes such as Campbell and Deadhorse (Gearhart Wilderness) are nice places to visit and escape the heat, but if the season is dry, fires are prohibited.
I hope this information helps!