Stacey here is a link to some Beech Mountain rentals that are pet friendly
http://www.homeaway.com/search/refined/ ... red#sp=691
Any place you go during Christmas will be crowded, that is just a fact of life. The secret will be to get up early, ski until about 2. After lunch is when it is most crowded. Do you have kids and if so how old? You also need to decide which area you want to go to (how far do you want to drive?
Asheville NC area has Cataloochee Wolf Ridge (both about 45 minutes from Asheville) and is probably the closest to FLA but also to Altanta so it will be the most crowded, also no slope side accommadations at Cat, I have never been to Wolf.
Northern NC mountains has Beech, Sugar and Appalachian all near Boone, all have good ski schools, all have close accom. I prefer Beech as I have a season pass there and they have great school plus a sledding hill in town.
If you want to go further north there are several Resorts in VA and WV, I have only been to Winterplace and Snowshoe. I would not choose Winterplace during a holiday and there are few accomm near. At Snowshoe it is a resort destination, so it may not be pet friendly.
There are lots of other resorts that I have not been to so others will need to chime in on those.
Hope this helps a little.