If it were me, I would give her a choice. She can either have a 4-6 person party where they all get to do something special (movie matinee, ice skating, or whatever you can handle a group of kids doing), OR she can invite her whole class but it will be a shorter party and held at X location (I'd advise scouting out places and prices ahead of time so you don't promise her something that would be out of your budget for 15 kids). Inviting everyone may be very important to her - or she may want to just take her closest friends and do something more special.
If you do decide to have 15 kids, I definitely recommend taking them somewhere you get an adult or teen to help - either a business that does parties (like a number of fast food chains do), or a public place (sledding, maybe?) and hire a "babysitter" to help you make things go smoothly. That way you don't have to worry about whether parents are or aren't staying, and if there's a troublemaker you won't have to divide your attention between him/her and the rest of the group.
Actually, this gives me all kinds of great ideas for snow-based parties
Have all the kids help build a giant snow fort in your front yard or a nearby park, do a snow hunt*, play "fox and hares**," have a long jump competition to see who can leave the farthest distance between bootprints, etc. Then come inside for hot chocolate, cake, and opening presents. Best of all, it's free, and you can have any number of kids participate
* A snow hunt is when you take a number of small objects, like wrapped hard candy or small plastic toys, and throw/scatter them in the snow. The kids tromp around the yard trying to find them all. Pick something that won't hurt your grass if nobody finds it before the snow melts
If you do it in an already-tramped area or on a day there isn't a crust on top of the snow, they will sink in and not be immediately visible from the starting area.
** Fox and hares is essentially a game of tag on a track in the snow. You make the "track" by shuffling your feet in a large pattern of unbroken snow, something like this:
The game starts with one kid "it" (the fox) and everyone else (hares) spread out somewhere along the track. The fox tries to tag one of the hares, who then becomes the fox. Everyone has to only step on the tracks that were already stamped out, though, so there's some strategy involved with a number of people playing, since it's hard to get around someone else who is already on your leg of the track