Are restriction enzymes active at −20 °C?
Enzymes have temperature optima based on the organism they were isolated from. So I would predict the there is virtually no activity at −20 °C. Another consideration is that the reactions are likely to be frozen solid, so that would limit diffusion, and also slow it down. But the real question is: what are you afraid of? Just the star activity? Even if there were star activity, would that adversely affect your experiments?