I play violin in my school's orchestra and that requires me to bring my violin back and forth between my house and school, which exposes it to harsh temperatures and drastic differences in humidity as well as temperature. All of this causes my violin to go out of tune quite often and in the winter it has problems staying in tune, which gets real old real fast. Is there anything that I can do so that will help it stay in tune?
Since the issue arises in the winter, the problem may be humidity changes. You could try using an instrument humidifier like the dampit to keep the humidity of the instrument stable. I've used them with acoustic guitars and they do help with issues that arise due to the drier indoor environment that can occur during the winter months in temperate climates.
I agree with all the suggestions you've already received. If you try these and still have problems you may want to get peg drops which will help your pegs stay in the peg holes and not slip. Be careful with these as too much (or using them when they aren't needed) can make the pegs very difficult to turn. Without seeing your instrument it's hard to know if this would be helpful or not. A luthier would be able to give you some more advice about this.
Are you walking or riding a bus/car? If you are walking or otherwise dealing with extended time outside, consider an insulated overcase cover. That should help with the temperature variations. There's not much you can do if the school is overly hot/dry, other than keeping the violin in its case except when playing.
Now, it's not quite clear that weather is causing all your tuning problems. Unless the violin stays in tune over the weekend (when it's presumably in the same room in your house), you may simply be dealing with slipping pegs or aged, dying strings.