There is a $15 registration fee for 3 years - and tax on your purchase. If you can get the person you buy it from to write you up a reciet for less than you are paying them then you can scam a lower tax fee. No insurance or anything like that though.
I ususally store mine when it gets too crazy cold and snowy - it's really not good for the moped to be out in that overnight. I've been taking it to a shed that i have access to, but i think i'll be bringing it up into my house this year.
If you don't have the room, there are usually storage places that have little tiny spots for like $25 a month...and you'd only really need to do it for maybe 3 months. If paying for storage doesnt' sound like fun then just get a tarp or motorcycle cover for it. The main thing is too keep the water away from it - so that it doesn't freeze up inside of it and expand things it shouldn't....