Early May can and does often snow in the mountains of BC and Alberta, however if you wait a day it will usually be melted and gone. Always plan to spend an extra day someplace because of weather. The days can be warm however they will still get cool at night. .
June can also have snow, but far more infrequent, usually June is nice warm and comfortable weather, we love camping in June ( less kids around grin) My Oldest Daughter lives just west of Calgary towards Banff and 2 years ago on June 2nd they got 6 inches of snow. The next day it was gone.
July and August are the best but way more people RV's and everything else that goes with the Summer. August 2015 we were at the kids place west of Calgary and we woke up to a clear sunny morning. Sitting on their sundeck we could see the Rocky Mountains around Banff had a fresh dusting of snow, later that afternoon it was all gone.
September is usually nice, warm, but nights start cooling down. Where we were camping last weekend there was snow on the mountains above our campsite on Saturday morning. To give you an idea of how far north we are in Canada, the Campsite is a 4.5 hr drive North of Spokane Wash, so we are not that far up in the great white north.
Traveling is 99% of the time just fine to travel between May and September, but like I said it can snow in any month of the year. Usually if you just stay an extra day someplace or wait out the weather it is "usually" better and the roads good to travel on.
Campgrounds start opening up usually" around the third Monday in May which in BC Victory Day long weekend and that the weekend that most of us Canucks that have been snowbound all winter break out the RV's and head to them campgrounds that just opened. "IF" you plan on being in BC and or Alberta on that weekend you "should" make a reservations someplace and stay there for the weekend. BC provincial campgrounds for all long weekends make you reserve and pay for all three days of the long weekends, not sure about our National park system ( Banff / Jasper for example) I haven't camped in them for a few years. However if you are in a Campground no matter where you are on any long weekend in Canada I would plan on spending the entire weekend as if you happen to leave and drive someplace else, you may not get in or be stuck in over-flow. There is the option of boon docking, so there is that option.
Also a "some" campgrounds start winding down after Labour day weekend so just be a wear of that.
Also you should be aware of Canadian Sat holiday weekends because Like I said us Canucks come out of the wood work camping as do the rest of the RVing public, so site will be at a premium. Just google them and write them down on your calendar to be reminded. This last July 1 ( Canada day) three USA RVers showed up at our campground looking for three spots to camp in. Well the place was full to the brim, but the owners found a spot put in a field for them to spend the weekend after she explained what was going on. July 4th is not a sat holiday up here ( grin)
There are other how live farther north and travel more frequently up there like, Sue in the Yukon who can answer you.
Soup.
2018 Northern Lite 8-11 EX Dry Bath
2017 Sierra SLE, 3500 HD / 4x4 / Duramax with a 6 speed Allison Trans
Torklift Super Hitch 20K, 48" Super Truss, front and rear frame mounted tie downs
Fast Gun Long Range SS Turnbuckles, Fast Gun locks