Conditions can be anything that time of year. I.e you can have bluebird & sunshine with summer-like conditions in front ranges, or you can have pacific front coming over from BC dumping half of meter of snow.
As a general rule of thumb: North side of Bow Valley above Canmore tends to be drier (it is half dry even now); this makes peaks like Grotto, Lady Mac etc feasible early season scrambles. In the other side of valley Ha Ling / Miners Peak
is done year-round, but could be icy. Similar idea with East End of Rundle
(EEOR). In the Foothills Yamnuska area (Yam, Doorjamb/Loder, Association, ...) is equally good.
In Kananaskis Porcupine Ridge
or Midnight Peak
are good choices that could also be dry. Smith-Dorrien corridor will have considerably more snow & I'd probably stay away that time of year.
Around Banff Minnewanka shoreline trail with hike up to Aylmer lookout
is personal favorite & I do it every year around that time.
Louise area will have snow with fair possibility of avalanches. Ski Tour (or snowshoe trip) into Skoki would top my list of recommendations. Heather Ridge
would be one idea.
Finally further up on Icefields excellent choice is trip to Glacier Lake. Water is low & you can walk along Howse River flats
; it is very scenic and very historic.
All the trips I mentioned & linked were done that time of year (+- 2 weeks)