Any suggested or advise...we are planning on dropping off dog at a friends house in Page for the day so we can explore Antelope Canyon and Lake Powell. Any other suggestions on where we could go or activities to do with our dog...he's a chihuahua-minpin. How cold will it be mid December?

Dogs are allowed in Grand Staircase Escalante and Vermillion Cliffs. Are you based in Page the entire time? The trailhead for Paria Rimrocks aka Toadstools isn't far from Page. Old Paria is a pretty drive and you can wander around but there isn't much left. There's still an old cemetery. Kanab is a cute town. I haven't hiked in Vermillion Cliffs, only stopped to watch condors.

i think you can take them on any BLM owned land. You can search the BLM website. It won't get below 30 degrees in December during the middle of the day. We go to Moab in February every year and its in the 50s-60s. Very nice for dogs.

If by "explore Antelope canyon" you mean having the freedom to stay in the canyon on your own. it won't happen. The upper and I believe the lower canyon can only be scene as part of a guided tour of about one hour. There are special photography tours that are longer, but also more expensive. I am not sure that they are worth it. Taken during the regular tour:

https://flic.kr/s/aHskaZsbGx