Here you go but the snow is for this THU-SAT:

http://www.theweathernetwork.com/wea...ta/lake-louise

Could still change and is very elevation specific for snow. You will also likely have more chance of snow at Bow Summit and the Columbia Icefields as the temps will be lower there.

Moose tour is an awesome way to see the Parks as long as you are part of or do not mind a younger demographic. Weather is variable in the mountains at the best of times but end of June you should have good hiking options, although with Moose you won't be doing any classic full day stuff unless you decide to hop off and stay a day somewhere. The Wilderness hostels are a unique experience.