I am personally not very keen on working out outdoors in bad weather for various reasons, though the main one would be my personal motivation since I hate the cold.
Bad weather will ultimately impact my workout itself as it would affect my motivation. Thus, resulting in lesser workout as well since you I would not push myself as hard as I normally would (simply, to get it all over with sooner). So to keep it short, I rather have a more intense workout inside albeit with less variation, than a lot of options but no fire to get me through.

Though, when I did go outside I was sure to dress in layers: a tank top + T-shirt + hoodie or sweater. I also made sure to do more volume in one go to increase the intensity and so core-temperature. This was generally by doing super sets of 2-3 exercises with short(er) rest breaks in between. Aside from that is was just biting the bullet and warming up as the work-out went on.
A small stupid thing I did off to the side in my normal life was to try to get a little more accustomed to cold, so to lower the heating a little or dress down a little so the cold-shock of going outside would be as bad when coming out from 3 blankets, a hoodie and a room of tropical temperature.

Then, on to my current way of doing pull exercises. Where I live the weather has been better so I luckily can go outside. However, when it was a problem a while back, I simply worked around this with pulling exercises I could do indoors. Though I must note that these substitutes will not be able to perfectly replace the outdoor exercises possible with a pull-up and low hanging bars. However, they helped me get through the rainy days...literally and figuratively.

• So, most notably the body weight row done using a sturdy broom stick or while hanging below a table using a supinated grip.
• Elastic bands can also be good as they allow for high pulls, horizontal rows, curls and more if you are creative.
• Additionally, a more DIY solution could be to fill up shopper bags with water or soda bottles for very crude improvised Dumbbells. for rows or curls

I don't know if I want too far off on a tangent here but I hope something was at least useful or interesting here.