McDonald's can be frozen for up to 4 months. McDonald's beef burgers, chicken burgers, and French fries freeze well, but you will need to remove any salad or dressing before placing them in the freezer.
If it's ice-cream based milkshake, like the stuff you get from McDonald's, neither will keep it right. In the fridge, it'll melt and turn to sugary milk. In the freezer it'll turn to ice-cream. Your best bet is to go with the freezer, then accept it'll need some time in the fridge before it'll go through a strawer.