There are two questions here:
- Is it safe for your body?
- Are you or someone else safe when on the traffic with you riding in the traffic?
For (1), I can say winter riding feels cold -- the colder it is, the less weight your body has and the faster you go, the colder it feels. You have all the time to have appropriate clothing. The difference between too little and too much clothing can actually be rather thin, and neither being overdressed (you become sweaty) nor being underdressed (you are in the danger of frostbite on hands or feet) is fun.
I recommend avoiding long bike trips when it has become suddenly much colder than it used to be. If it was +2 and now it's -8, please do only short trips to ensure you are properly dressed and once you are confident, you may do long trips at -8.
The most important parts are your hands and feet. Your lower legs and arms should be covered by thick clothing and whatever shoes or gloves you have, they must be tight. Any air gap puts you in danger of frostbite.
As for pants and jackets, you may need several. Some materials to consider are wind-proof materials and thick fleece. Sometimes, I wear both: a wind-proof jacket and a thick fleece jacket over it.
For (2), please, don't cheap out on tires. If you have a BSO, you probably haven't invested a lot of money into your bike. Please do buy proper studded tires, preferably the thickest ones that fit into your bike. Don't cheap out on tires. If there are two studded tires with one having less stud rows and smaller tread blocks, pick the one with more studs and thicker tread blocks. Also experiment with tire pressures: generally winter tires are run with a very low pressure that creates lots of rolling resistance (except on good days you may increase the pressure for reduced rolling resistance).
However, there are conditions where riding even on proper tires is unsafe. Here's a video of someone trying to ride on such conditions on a fatbike:
Snow that has been unevenly packed by pedestrians walking on it in a thin line is generally unsafe. Snow that has been compacted and then partially melted into snow-like slush is unsafe. Basically, only ice, fresh snow that has fallen and not partially melted, and plowed roads are safe -- and if your tires don't have studs, ice is unsafe (even with studded tires but no studded shoes, you can fall on ice when stopping at a traffic light for instance).
If lots of pedestrians start walking on the road before it becomes plowed, it may become unsafe. If the snow partially melts before it becomes plowed, it may become unsafe. Generally at the end of the winter, when most snow has melted but there are some sections of snow-like slush, it's unsafe to ride over those sections but you can walk your bike over those if you just take the time to stop.
Two kinds of problems, (1) is attacked by proper clothing especially on your hands and feet, and (2) is attacked by wide low pressure studded winter tires with deep tread blocks.