BUR has never had jetways and is thus outfitted with various boarding alternatives to stairs. There are low slope switchback ramps that are ADA approved for wheelchairs and I've seen special forklift-like equipment deployed to the opposite side forward door if the ramp isn't working. Passengers needing assistance is an everyday affair at BUR. They know how to handle it. In fact, I'll contend that for this among various other reasons involving size and convenience, BUR should be your first choice in LA, if the choice is available.
Also, you'll never ever have to deal with icy weather at BUR.