As you can see from the photos below, I have a pot problem. Are there any adhesives which can withstand the heat/sun of summer and the freeze/thaw of moist winters?

I have the same problem. After a few years my ceramic pots break due to the freeze/thaw cycles. I think if you repair the pot (which is easy to do with most types of waterproof epoxy or glue) it will just break again in another spot.

Plastic pots last much longer for me. I try to buy those that are made of recycled plastic. Or I buy "rescue" pots at yard sales, etc.

I've seen videos where they've used JB Weld Epoxy (the 2 tubes where you mix them together), and they seem to swear it works well. I've seen videos where they've repaired outdoor bird baths and it's held.

I've also read about using Liquid Nails, but most often I find info where they used JB Weld.

Gorilla polyurethane glue would be excellent as long as you're not too particular about whether or not any of the adhesive shows on the outside of the pot. If the cross-section of the broken piece is porous clay, spritzing both pieces with a fine water mist before they're glued and adhered will speed/strengthen bond formation.
Al

Why not just leave it how it is?

If you're not using it (or any other pot) for winter, turn it upside-down, or put another pot upside-down over it, or some other kind of cover. Then they can't get wet enough to expand when frozen.

I just got it and will be using it at some point. I just want to do the repair well in advance of needing it.

I have had great success with a product called Big Stretch. It has great adhesion and the extra stretch will cure the freeze thaw at least at the repair site

I recommend Flex Super Glue. You can get it at Lowe's and it's great. It says on the package it bonds plastic, metal, ceramic, leather, wood, paper and more. If it doesn't work you can get your money back. No problem! I glued the soles of my walking shoes back on and it was super fast. You have to hold it tight for 5 to 45 seconds.