Generally, we think of that requirement in terms of number of days with temperatures in the 32 to 45 degree F range. Until their need gets met, plants won't break dormancy, no matter how warm it gets. The results of late-winter warm spells are less dependable, however. Some plants tend to bud out earlier than others. Different plants' buds vary in how 'tough' they are.
Harsh cold can kill.
It also can slow new growth, but leave it largely unfazed. Typically, what gets caught first is the flowers on some established trees and shrubs. Apples, crabapples and forsythias have tougher buds. So, they can be the reason Kansas still puts on a spring show, even after a late winter that included extremes of both warm and cold.