We travel from the Rio Grand area in Texas to Chicago in March and back in October. The DW will not miss the grandchild's birthday and we both agree to not staying for snow in Chicago. Ours is a very planned event and one must have many options at the ready. Although our inverter will power the furnace when traveling and we could run a space heater too, these options are at the bottom of the list. The norm is to travel in daylight when temps are above freezing and then camp over night when temps drop below freezing. Not as many miles are accomplished this way but it is safer.
Have a good review of each area you stopping for the night "with reservations" (If possible), this I would say is at the top of the list. Talk with the manager of each campground so they are aware of your plans.
Two other items are in the bag #1 weather, #2 emergency. Not much to talk about the weather but extended stays are possible and is always discussed with campground management when making reservations. Practice on winterizing in an emergency. Have you winterized your RV before? Are you sure it's good to go? I have had to winterize in a Walmart parking lot (Victoria TX) due to dramatic weather change and a family member passed away. It turned into an emergency to drive longer than expected.
As I stated before, one cannot have enough options when traveling during the fall to winter months or winter to spring transition periods. Good Luck.