We are CA natives who lived in Boise for 5 years ('05 to '10). We now live in Northern California, about 200 feet off of I-80, on the Western slope of the Sierra Nevadas. We did the drive from Boise to
Disneyland twice during the 5 years that we lived there.
Personally, I would not do that drive in the Winter. If you take the South-through-Utah route, there are several areas where bad weather is likely and can make the drive quite dangerous (the pass around Snowville, further south around Beaver, and the stretch between Vegas and DLR, no matter which freeway you take).
If you take the East-through-oregon route down into nevada and onto I-80, that stretch between Boise and Winnemucca, NV can be absolutely treacherous (and I know this from experience, having been caught in an unforecasted blizzard once, which caused us to spin off the road into a ditch with our 3 young children in the car). Even if you make it to the 80 without issues, the pass between Reno and where I live now (just on the other side of the pass) can be an extraordinarily dangerous stretch in poor weather, and often is closed during the Winter. Chains are almost always required during Winter, and often even into Spring. If you get through there without issues (if you manage to dodge through between storms, that is), then you still have to deal with the Grapevine on I-5 (which is also often closed when it snows).
I love Disneyland, but it isn't worth the dangerous drive that is required when driving during Winter from Boise, IMO.