Of course with a terrorist attack on the death star perpetrated by a boy from Tattoine, his friend from tattooine, and assisted by two mercenaries from tattoine, the empire really had no choice but to invade Hoth.
Some people might have thought the smart money was on waiting on tattoine for them all to come back.
Sure, there is a chance it would take six years or so for that to happen, but far fewer stormtroopers would have had to die on foreign planets.