If you want to book ahead, I would buy a ticket to SLC. Skyline is already open and with a couple more storms it will be solid. Strawberry still needs more snow as there is sage brush to cover there. Sometimes, it opens early like last year, most years it is not ready until Christmas.
You are still early enough in the season, that you can get a hotel in SLC without a prior reservation. I would wing it and book each night according to the weather. If it looks good at Skyline for a couple days, book a hotel down in Mount Pleasant. If not, stay in Sandy near the 106th South exit. This will leave you close to Alta/Snowbird and 90 minutes from Skyline or 75 from Strawberry.
As far as kites go, we typically fly large kites because the winds tend to be light. That being said, it can still nuke every so often. So the bigger the quiver the better.
Bighorns are awesome, but I agree that you might be biting off too much if you have not snow kited before.
Best time to come out west is in February. That is when Strawberry is sweet and you can also road trip to lots of other awesome spots in Idaho, Wyoming, and Montana. That being said Skyline should give up some excellent riding in December.