Keeping warm and comfortable overnight in the cold is the product of a couple factors: generation of heat (usually your metabolism from your dinner and snacks, but can also be an external heat source like a hot water bottle or wood stove) and retention of heat or reduction of heat loss from conduction (sleeping pad), convection (sleeping bag or quilt, and tent or tarp), and evaporation (staying dry).
Generating heat
It’s important to eat a high-calorie meal when in the cold, and supplant it with warm drinks. Having snacks like cashews in your tent and easily accessible can be a great way to stay warm over night and if you wake up chilly. Typically animals will be less active in the winter months, but consider the possibility that you will have an uninvited visitor overnight, possibly chewing through your tent.
“Hot tent” camping involves a small wood stove inside your tent, with a stove jack to protect the tent material from the hot chimney. This requires an investment in a pretty big tent and stove, and the ability and enthusiasm to transport and set up everything. So that is the how. But should you? In my opinion, it’s only worth it if you will be in the same location for multiple days, and the temperature is into the teens; typically hunters and backcountry skiers going on multi-day trips fall into this category.
Retaining heat
Starting from the bottom… An insulating sleeping pad is an often overlooked, but critical component of your sleep system. Sleeping on the cold ground will cause heat loss trough conduction, or the direct transfer of heat from a warm object (you) to a cold object (the ground). Sleeping bag insulation is compressible and light weight (which makes it good for packing into a backpack), and your weight will squish it down, rendering it pretty useless for insulating against the ground. Look for a sleeping pad with an “R-value” of over 5. Wes Siler on Outside Online has a great overview, as does Outdoor GearLab, SectionHiker, REI, and Switchback. I have the Exped DownMat HL, which has an R-value of 7.1 because I sleep cold and have a different pad for warmer temps. Feel free to double up on pads (foam with an R-value of about 1.5+an inflatable one) if you don’t have a dedicated winter pad and bulk isn’t an issue.
Your sleeping bag (and underquilt, if you are in a hammock) will reduce heat loss from convection or transfer through air. The down or synthetic insulation of your sleeping bag creates pockets of warm stagnant air near your body. Look for a sleeping bag with an EN rating about 25 degrees below the temperature you expect to encounter. If you can afford it, go with a down bag; modern down bags are less susceptible to moisture, they are lighter, and pack down better. That said, I have the zero degree Mountain Hardware Hotbed Torch that I bring if the temp is going to be in the 30s or below. It’s synthetic, cheap, and great for car camping, although I’d probably want a down bag if I were hiking anywhere too far. The EN rating is really the minimum temperature that a person that typically does not get cold at night (“sleeps warm”) could theoretically be OK in if they were wearing layers and a hat etc. Summer time, I am in a 30 degree REI Magma quilt, Fall and Spring (“shoulder seasons”) I am in a 20 degree EMS Solstice bag, and 20-30 degrees I am in my zero degree MHW bag. You can double up bags if you have a light summer bag and medium weight shoulder season bag, but it’s kind of bulky and I would not recommend it. You should also be in some warm fleece jammies, fuzzy socks, and a hat; they are part of your sleep system too.
Your shelter will provide protection from the wind blowing against your sleeping bag and cooling it off. You are basically trying to strike a balance between one that blocks breezes but also one that allows some air to circulate so that the moisture from your breath and sweat does not build up and condense on the tent walls, freezing or dripping down onto you. The most primitive and small is the bivy sack, a type of wind barrier that is essentially a body bag, and in my experience clammy and not that comfortable. Next step up is a floorless tarp-style shelter. These work in the winter because there aren’t bugs that will crawl on you from the ground, they vent well (sometimes too well), and are light weight and simple to set up. I have had good experiences with my Black Diamond Mega Light, and have a Mountainsmith Mountain Shelter LT. The larger ones are great with a small cot, to get you off the ground. Finally, a normal tent with a bug net and floor. Unless you are in heavy snow, you are probably fine with a “3-season” tent, it’s not really going to be insulating you anyway. A single-wall tent like my Sierra Designs Flashlight 1 FL has just one layer of fabric between you and the outside, a double-wall tent is a mesh bug net and a rain fly; these don’t really insulate any better, but they reduce the chances that you will get condensation dripping on you overnight. you can also bring a bivy sack or trash bag to sleep in, they will both have similar comfort levels.
If you are in a single wall tent, venting and site selection is extra important to staying dry. Basically for winter camping, stay away from bodies of water that will be humid, valleys where cold damp air will collect, and ridges that will be windy. When camping on Virginia’s New River Trail, my dad and I camped right next to the river, which was cool in theory and humid, damp, and cold in practice. Waking up with soaking wet tent walls dripping condensation onto your sleeping bag isn’t super fun. Andrew Skurka has a more in-depth piece on site selection.
Most importantly, don’t be afraid of cold weather.
Practice with your gear and figure out what works for you in a low-consequence situation like my quick overnighter on the C&O Canal, where my car was a few feet away. In all likelihood, the worst case scenario is you are cold and don’t sleep that well, but you’ll survive and learn a lot! For further reading, Wes has a great piece on Outside Online that covers most of this stuff; I really like his articles, they are written in an accessible manner and cut through a lot of marketing and technical speak that can be confusing. Good luck and have fun.