Hamster in the Snow? Please help me?

Hi I have a 2 year old Fancy hamster who is a girl. I live in Illinos so now its snowy / snowing. I always take my hamster outside in the summer or when its not bad weather cause my hamster book says its okay too. I have not taken my hamster outside in this weather which is fall but it is like winter cause most days are about 20-30 degrees farinheit. I have not taken her outside in this weather but is it okay too?Can they go in the snow? I dont think they can but Im just checkin. And if they can/cant how hot and how cold in farenheit can they be outside? Thanks sooooo much!