what is a good and reliable way to measure body fat?
The devices that measure electric resistance are the least reliable way. The most common way is to have an expert measure the thickness of a flap of skin on a few standard places and calculate a Fat% through a table.
The most reliable way is a test where they put you under water and calculate Fat% by the volume you replace and your weight.
To answer the first question: Winter is a good time to lose fat, but winter is also a time when diseases lurk. If you train too intense and compromise on food consumption, your body will recover badly and your resistance will also drop. An illness would set you back more than a percent of fat more, I can tell you!
So: Be careful not to train too intensely, make sure to keep a diet that contains enough vitamins and minerals. Those that exist naturally in your food are better than artificial products, but that said: Most books on training advise to supplement during a weight loss fase. Also: Do not lose fat too fast. According to most training methods, you are able to lose something like half a kilo a week, without compromising performance.
Your question "how low can I go", can be answered by "just as low as you can, without getting ill or compromising performance". I would be on the safe side if I were you and not focus on a minimal Fat% too much.