Goat question....?

My goats were really cold and shivering, so I looked on ebay for goat blankets (like mini horse blankets). But they seemed overpriced to me, so I went to Dollar General and bought men's sweatshirts and put them on my goats. (I'm serious!) They fit really well, but is it safe to leave them on my goats while I'm gone? Could they get hung up on something, even though the shirts aren't baggy on them? Serious answers, PLEASE! :)