Thinking about seedlings under 4 feet of snow

It just keeps snowing! I look out my back window and try to imagine a lush healthy vegetable garden where a blanket of white currently resides. I am shopping for seeds and trying to plan what will go where while the icicles hang long and menacing from all around our house. This will be my first garden to plant myself and I really had no idea how much imagination I would need.
I will be a new mother in one month. If everything goes according to plan I would like to feed this little guy nothing from a can. So the plan is, when the blanket of snow finally melts, I will plant tomatoes and squash and peas and carrots and broccoli and spinach under my apricot, peach and cherry trees. In seven or eight months, inshallah, when this guy is ready to start sampling the wonderful world of whole food, I will have some interesting and healthy things to start feeding him that I grew from my own blood, tears and sweat and that did not travel around the world to get to him. My hope is that he will not have to eat bananas that took more energy in fossil fuels to get to him than the calories they will provide for him.
I do not think this is a very lofty plan. My friends and family think I am a little crazy, but I am hoping it is doable. After all, here it is February and we have snow banks up to our shoulders yet I am still eating fresh apples that were grown within 100 miles of my house. If my tastebuds can make that stretch perhaps my imagination is capable of planning out a vegetable garden under a curtain of frost.