My VT700 has "issues" starting when temps go down below 50, and I have to use the choke/enrichment to get her to even try to start. In temps below 30, it is near impossible... I've come to the conclusion (since my Sabre and my son's NightHawk both start without issues in those temps) that the VT700 engines just hate the cold, lol. Even when I do get her running in those temps, the temp gauge barely hovers in the lowest point of the middle bar, even when I'm riding in-town speeds, and will barely reach that if I go 60mph.
Now that you've moved the lights from the main circuit, running them while the bike is in motion should not cause electrical drain as long as your stator and Rectifier/Regulator are working properly. Stock set up gives you about 100W to work with for "accessories", if everything is working properly.
I also agree, 20W oil is just too thick for starting a bike in those temps... I had 20W50 in my truck last year (hadn't changed from summer), and she absolutely refused to start if temps were freezing or below. I changed to 10W40 and never have any issues starting or running in any weather now. On my VT700, I've been using Rotella T 10W40 and 15W40, and it seems to be holding up quite well... easier starts when its cold out, and still have 40W protection when she's up to operating temps (and in warmer weather).
I'd keep a lower weight oil in her, and check the function of your stator and R/R to make sure you're getting enough output to maintain running those extra lights. As for your headlight... I'd make sure the main reflector (not the bucket where the wires are) is still shiny, and pop in a $4 Hella 60/55W bulb from Amazon (cheapest place I've found them... and they are the OEM bulb that was in my Sabre)