In the Kootenay Plains area, the nearest overnight hike would be Kinglet Lake. While there may not be much snow on the plains, expect it to be snowbound around the lake until mid-May.
The Ya Ha Tinda area is another possibility. I spent a night at
Eagle Lake in early May several years ago and didn't need snowshoes. I did, however, wish I had hockey skates, stick and puck for the smooth ice on the lake. If you stayed on the north side of the Red Deer River, I'm sure you could wander some distance before running into a lot of snow, and the south facing slopes could be hiked for some good views.
But I agree with Rachel, March will be prime ski season in the Rockies.