What they all said.
I'm still skiing up in the high country at that time.
You are going to have to look lower.
Not extreme backcountry by any means, but Golden Gate Canyon state park is (generally) 9k ft or lower and is a possibility not far from Denver. There are "backcountry" campsites you can use. With the early season wildflowers that may be poking out, could be pretty. It is where I hike in mid-April or so until summer at times (and late Fall. It is also where my wife and I married. :)
Even there, the higher elevation areas in the shade may have some patches of snow. Should be doable, though.
Other possibilities are the first sections of the Colorado Trail. But, quite frankly, that is mainly mellow MTBikng terrain. While pleasant, I think Golden Gate is more interesting.