Galveston TX - Grand Canyon National Park AZ Roadtrip

[Shilpa Krishnan]

Hi everyone -
Me and my partner are planning to go to Grand Canyon and Zion national park via road from Galveston, TX. We will like to camp on our way to GC in state or national parks or any park/river that is safe and scenic. As of now the plan is to travel from Dec 24 - Jan 2. We want to reach Galveston back by Jan 1 or 2nd since my partner has to fly back to east coast. Depending upon the suggestions we may take additional days off.

This is our tentative plan:

Day 1 Galveston - Carlsbad National park - 10h12m camp somewhere near Carlsbad NP ? suggestions are welcome.
Day 2 Drive to Lincoln National forest - 2h 42 min and camp there
Day 3 Camp at Metor Crater - 7h30min (441 miles) or Go to Petrified National forest 6h44min (372 miles) and camp overnight
Day 4 Go to GC - 1 h 51 min (112 miles) from Metor Crater Petrified forest - GC us 2h50m(177 miles)
Day 6 drive to zion national park - 2h 3m (98 miles)
Day 7 drive to Sun rise lake 6h40m (400 miles)

Although I have listed the places I will like to visit it looks like a bit much. The whole idea of road tripping is to camp and enjoy the scenic places along the way. I am not sure how these places will be during December, will it be too cold to camp? Will it be snowing? Any suggested camp grounds in my areas of interest or any other? Please suggest.
If any of you know a good route to take to avoid the rough winter I will appreciate it, since we will be driving a Toyota Corolla for the trip we want to make sure we don't come across passes and are trapped.
Any other suggestions on places to visit are also welcome.