We have done Calgary to Arizona quite a few times since 2001. In January you need 3 days of clear weather. I15 is well maintained. If there is snow they generally have it cleared within a couple days.
We always leave I15 at Boulder MT and do highways 69 & 41 to Dillon, Mt. This lets you miss 2 of the passes on I15, near Butte. This route is good 2 lane highway, used by lots of semis.
We have always stayed in the RV. There are a few RV parks that stay open year round - Great Falls, MT (Dicks), Dillon, MT (Countryside), Nephi, UT (High Country). You mentioned 89 - it is a nice 2 lane highway. You would leave I15 at Nephi to go south on 89. Definitely do not do highway 14 from I15 to 89 - it gets up to about 9000+ft - not good in January. If you decide to do 89 make sure the weather in southern Utah is clear of snowstorms.
When we did it - Calgary to Dillon is about 9 hours. Our second day would be Dillon to St. George - about 11 hours. We did 89 from Nephi once - it took about 12 hours from Dillon to Page, AZ. We pulled into Page after dark and just stayed in the Walmart parking lot. We had filled our fresh water tank at the Flying J in Nephi, so we were okay with dry camping for the night. The water system was winterized when we left Calgary, but DH had blown the RV antifreeze out of the system so it was easier to dewinterize once we got far enough south. We used rv antifreeze for the toilet and carried a 5 gallon container of water.
As others have said, monitor the weather forecast closely and be prepared to delay leaving for a couple days until you have a clear weather window. Travel safe and enjoy snowbirding.