I have two kids (about 70lbs/30kgs combined) whom I during the summer frequently took biking in a trailer (once I got them used to it, say a dozen trips this summer or slightly more). I biked 5+ miles round trip with them without significant difficulty; I'm not in great shape, but I was generally able to get up over 10MPH when I had a decent flat straightaway, and didn't need to stop (biking 3 miles in a residential setting with frequent stop signs/lights in 20 to 25 minutes). I typically bike in the 2nd forward gear, 4-7 rear gear (4 is for starting from a stop usually, then I go up to 7 once I'm at speed assuming I don't immediately stop again).
I hadn't biked for a couple of months perhaps, when I suddenly had a need to bike ~6 mi round trip to take my older son to preschool and younger to daycare. This was on a suddenly cold day, below freezing - around 10˚F/-10˚C. I checked my tires visually and by feel, and they seemed fine (the bike was stored in an unheated garage, but it probably did have a 20 or more ˚F buffer from the outside given this was the first day of real cold weather).
I made it half a mile, in 2nd and 1st forward gear, completely out of breath and almost vomiting.
I saw at least two problems: one is that it was as if I had shifted to 3rd forward gear, as far as how hard it was to use the gears - I couldn't go at all in my normal gear range. Second was that the cold air seemed to have significant effect on my lungs even after not very much exertion.
Are some of these issues things I can do something about, or is biking in the fairly cold impossible for someone of my skill level? Is the chain oil wrong and not functional at lower temperatures? Is the 70lb weight on the back of my bike making a bigger difference (due to air pressure in the tires or something)? I'm not taking into account ice or snow here - this was the first cold day of the winter, so just simply cold (this was during the 'polar plunge' or whatever silly name they gave it this year). I know exertion in the cold is a different beast than exertion in the summer, but this seemed a level of magnitude harder than I anticipated.
I have a hybrid with factory tires, ~$400 USD bike when new (now 2-3 years old), probably has maybe 200 miles on it total. No particular maintenance done recently, just usual tire airing.