Most states require bicycles to have a white light in front and a red light in back, both visible at 500 feet, as well as side reflectors and a red rear reflector.
White strobes are brighter and are visible at a greater distance but alone they don't meet legal requirements. Also, they blink less frequently, making it harder for drivers to see your position and direction.
Flashers are best mounted on your bike or rear rack, where they can be aimed precisely, rather than on clothes or packs, where they shift around. Many people install more than one rear flasher.
People who ride longer distances and in all conditions usually use more powerful lights. Generator lights don't work well in wet or snowy conditions and often don't give enough light at slow winter speeds. The less sophisticated ones give no light when you're not moving.
Try to pedal smoothly and relax your upper body, especially on ice and soft snow.
When the bike starts going sideways, make small corrections rather than over steering and weaving down the trail. Practice riding in a straight line when the trail is good so it's easier under bad conditions. On some soft trails, higher speeds take less effort than lower speeds because your tires sink into the snow less at higher speed. When riding in a group on soft trails, have the weaker, less skilled or badly equipped riders lead so they can use the trail before the better riders cut it up. Road ice can provide lots of traction or very little. Learn how the different types look and sound. Try not to brake hard on the slippery sort, or if you must, use only your rear brake. Watch for dry patches where you can do your braking or turning.
Cycling generates a lot of heat so clothes that are warm and comfortable have to control the buildup of heat and moisture as well as insulate and protect from wind. Your particular metabolism, physical condition and riding style will determine what's needed to keep you warm. Your outer layer on top and bottom should have a windproof front and breathable sides and rear.
Goretex and other "breathable" waterproof materials become clogged with ice at below-freezing temperatures. As windproof front materials these fabrics are acceptable but unnecessarily expensive. Multiple light layers with neck zippers let you adjust your ventilation as you ride. Your base layer (against your skin) and mid-layers should be synthetics or wool. Cotton in these layers will feel wetter and colder than the above materials. No T-shirts! Carry headband, hat and facemask and try them in different combinations. Uncovering your head is usually the simplest way to dump heat. You may need to change the sizing pads in your helmet or remove them entirely to fit your winter headgear. Some hats are made specifically to fit under helmets. Try taping over the vents in your helmet if your head gets too cold.