I think your best bet would be the Lost Creek Wilderness. April is still early but it would be doable with snowshoes (and some lower areas will be melted out).
A good thing about Lost Creek is you can put together a number of short or medium length loops if you only have one vehicle.
You need to be able to navigate if the trail is covered so have a good map and a real compass.
1. There are several options for short overnight trips in the eastern end of the wilderness using the Colorado Trail, the Rolling Creek Trail and the Wigwam Creek Trail.
The will be snow and the trail will be hidden.

The advantage of this area is that its not technical. The downside is the scenery isn't as great.
2. The Colorado Trail – The trail starts on the eastern end of the wilderness, cuts across it then skirts the western edge until it crosses Kenosha Pass at Hwy 285. The eastern end is in the forest (see the above photo). There will be more snow because of the shade.

After leaving the wilderness the trail is mostly on open ridgelines overlooking South Park. The scenery is better and you might be able to ditch your snowshoes. A lot of the dirt roads along the edge of the wilderness will be closed or impassible so there should not be too many people here.
3. There are some loops you could do in the Southwest corner of the wilderness but they might be tougher with snow. The terrain is steeper and rockier. Be aware that lots of snow could hide cracks between the many boulders. Don't fall in there
If you try this you can see the mountains from the roads in South Park which will give you some idea how much snow to expect.

This was mid May in a very, very low snow year.