The Snowy owl's main diet is lemmings where they live. In years when the lemming populations are low, it is not unusual to have Snowy owls in PA hunting for field mice and voles.
Actually, it is quite the opposite. Booming populations of lemmings, and other prey, lead to large clutches of snowy owls. After such a huge nesting season irruptions of snowy owls to the south occurred. These owls are far from starving and actually have been found to heavier and healthier than off-irruption years.