Replying to Bad Batteries or bad Camera

3 weeks ago I bought my first camera (canon vixia hfm40) off ebay because it came with 5 batteries, a wide angle, and was refurbished by canon for about 230. I love the way the video looks but only 2 or 3 of the 5 batteries actually work and they only film for about 100 min max each. This isn’t too much of a problem but when it its even barely below freezing it dies in like less than 10 minutes which doesn’t give me a lot of time to film on the east coast. The batteries seem to be pretty small (850 mAh) and i could buy much bigger ones for around 25 each but i don’t know if that would fix my issue or where my issue even comes from. if i were to return this one to get a new camera would my issue go away or would buying new batteries be enough to keep it alive. I would rather not wait to get a new camera in the mail but if it’s necessary to have a camcorder that stays alive i will. Any advice?