Even short-haired dogs can tolerate a moderate amount of time in the snow, but if it's Daisy's first experience in the white stuff, you'll want to observe carefully to learn her limits. With extended exposure, ice, slush and grit can get stuck between your dog's pads, leading to problems ranging from cuts to loss of traction and even frostbite.
Preventive paw care includes cutting nails short and trimming the hair between toes to prevent ice buildup. Don't try to dislodge ice balls when you get back inside; it's better to let them melt on their own or to wash your dog's feet in warm water. A product like Tuf-Foot will help build resistance to abrasions, while booties serve the dual purpose of preventing ice buildup and providing traction when the going gets slick.