Agree w/ 1acrefarm. It's definitely possible to be fully self-sufficient--we've got oodles of historical re-enactments of Colonial villages around here that were exactly that.
But it takes a LOT of land and a LOT of time and labor. If you ever want to find out, honest to goodness, how much space one human takes up just for heat and food, trying to be self-sufficient is a good experiment. You can grow a mighty big garden and get particular breeds of animals that tend to eat whatever grows readily on the land you've got. You can set up a freshwater aquaculture system for fish. You can maintain hardwood species in a woodlot for coppice and firewood, and get a really efficient woodstove. You can cook maple syrup, raise bees for honey, and grow sorghum and sugarbeets. In a cold-winter climate, these activities alone will take up at least 60-75% of your waking hours, if you're fairly clever about building things to make chores easier, are lucky with your land siting, and get a family member or two to pitch in. Also, you have to be REALLY not too picky about food, because eating potatoes, pumpkin soup and cooked kale for three months straight in winter is very very tiresome. All of a sudden, things like ice fishing and hunting for hours in the dead of winter don't look so bad, when your other option is reheated canned baked beans for the hundredth time.
And then you have to figure out what you're going to do for textiles--blankets and sheets tend to last a long time, as do towels if they are good quality. Back in Ye Olden Dayes, one or two sheet sets and towel sets used to do for a whole family for an adult lifetime (admittedly not that long). Felted wool goods are considerably easier to make than spun and woven/knitted thread, but they don't last as long and need special washing. And trust me, wool undies are a bad choice--I don't know about you, but I need more than a couple pairs of undies to get me through a year, much less a lifetime. So you'll need to grow cotton or flax, and process it. Cotton is easier to process and spin than flax, but doesn't last as long.
Sewing and knitting is an entertaining hobby if you've got the spare time, but if you've just spent 10 hours cooking, cleaning, weeding the garden, minding the animals, pressing your oil crop (olives? sunflower seeds? peanuts? canola? algae? depends on your soil and climate, but you'll need several acres dedicated to it), you've only just gotten a chance to put your feet up and have a cuppa, all of a sudden the prospect of staying awake for another two hours to bloody KNIT because your socks got a hole in the heel is not so entertaining. Traditionally, fiber processing was done by unmarried women in the household, while married women did the cooking/cleaning/gardening side of things. (What men did, or rather failed to do, is a whole other rant, I'm just saying I'm glad I live in modern times and my husband is good about housework.)
Basically you need a live-in servant or three, otherwise this role was supplied by your extended family living with you. When your extended family lives in one house (same size as modern houses, BTW), you still only need firewood to heat one house, so it frees up fuel-harvesting time. If a few family members work in the Big City, and they can carpool to work, that cuts down on the amount of oil crop you have to grow for diesel. Personally, I am happiest when my mother lives about three states away from me, and I love my granny whenever I can outrun her. So total self-sufficiency would not work for me.
We do have a woodstove that partially replaces the oil heat in winter, but we still need oil heat for a backup. I have a big garden, DH trades services for local venison and I fish. And of course there's plenty of eggs. But we'd have to both be starving--and have live-in unemployed relatives--to make any more than that realistic.
