I will be looking for warm climates in the winter.

Big Bend looked good for September and October.  November and December look good in the Amistad National Recreation Area  near Del Rio, Texas.

“The coldest day of the year (in Del Rio, Texas) is January 4, with an average low of 40°F and high of 61°F.”  That sounds do-able.

And Texas has sweet fishing rules: “A fishing license and stamp endorsement are not required if fishing from the bank in a state park or in waters completely enclosed by a state park.”

Here are 2 nice sounding camping spots:

Rough Canyon
4 sites; each with a covered picnic table and a BBQ grill. The sites are suitable for tents or RVs. No drinking water or hookups available. Each site costs $4/night. ($2 with a Senior Pass)
Spur 406
6 sites; each with a covered picnic table and a BBQ grill. The sites area suitable for tents or RVs. No drinking water or hookups available. Each site costs $4/night. ($2 with a Senior Pass)

Click on image to get a big picture

There are many advantages to this area, aside from fishing and weather. Del Rio has a UPS store, there is a library and grocery stores. I can stay for 14 nights in one spot, and 60 days total per year.
Sounds pretty good for winter, even though it costs $2/night. That is $60/month. Another budget adjustment time. Since I will be driving only 200 miles for these two months instead of the 1200 miles budgeted there is a big gasoline $ saving of  over $250. Enough savings for some fishing equipment!