No offense, but do you honestly think your parents are that stupid? You plan on having a guy sleep in your shed for two weeks, bring him food, and hang out with him away from your home all day every day? And you think that they won't notice. Give your parents some credit, they're older and probably smarter than you. You will get caught.
Point two, I don't really know where you live but where I'm from if someone sleeps outside/without heating in December, depending on the night they could potentially get frostbite or maybe die if the weather is really severe. Depending on the weather he's going to be very unhappy. Short of a space heater you won't be able to do much about that, and you have to be very careful about make-shift heaters. I know a few girls who died from sleeping in a horse trailer with a faulty heater that leaked carbon monoxide.
Point three, why don't your friends know about him? That sounds pretty shady to me. Your mom doesn't like him, you haven't told your friends about him, and you want to hide him in the shed behind your house for two weeks? You've got to ask yourself why you are putting yourself in this situation. I really get the feeling that there is some reason why you aren't willing to tell your friends about him, and why your mom doesn't like him that you aren't telling us.
I don't want you to feel like I'm attacking you, but this sounds really sketchy to me. I can see it ending badly in so many ways. One of your family members gets something from the shed and sees him, your family notices you going out to the shed with food, that you're never home and not out with your friends (and if you tell that that you're out with so-and-so and that person calls you're screwed), someone sees a stranger going in and out of the shed, if it snows someone will notice all of the tracks by the shed... I could go on. Please think long and hard about the logistics of this and why you're doing it. I get the feeling that you have no idea what this is going to involve.