I didn’t have central heating or hot water in my home when I had a baby, we were often cold, we often slept in the same bed and room for warmth, we literally bathed using a kettle and a baby bath. We didn’t have a choice to put on the heating because it didn’t work, and if it had I couldn’t have paid for it. We had a three bar stand heater which could be used for a short time if I had the money to boost one room, we frequently slept downstairs to benefit from that.
Don’t let babies sleep in snowsuits or anything with hoods. Nothing wrong with mittens but use the built in kind. Several slim or thin layers work better than one bulky. The best way to stay warm is move, and keep your baby against your skin, so they will warm up too. Use a sling or baby carrier and keep moving. Move the furniture away from the walls to stop damp. Make sure the pipes do not freeze, ours did once and the mess was spectacular - but don’t worry, it was 3 degrees indoors that day and -10 outside so we are a way off that. Hopefully if you have hot water running through sometimes too that will help. If it’s colder indoors than out open up the windows and doors. Cover up all droughts and draw all curtains, hang more curtains over doors if you have them, sheets or towels if you don’t.
If you do have access to heating try to heat here and there, maybe for an evening or two during the week as if you do that the temperature will never drop too far down, boosting it up even a few degrees means it takes a while to drop off. That was my problem with it, with no heating or hot water to fall back on it never got boosted up and after a few months of that it’s as cold indoors as out.
do you have access to any schemes for warm homes or insulation? Are you on a priority register with your energy provider?