How Important Are Long Work Hours at Startups?

Depends on the stage. If you're super early - and not a founder you'll be expected and might have to work grueling hours (although be aware you'll likely never see those hours turn into $$$).

If the company has money, 3-4 months burn is reasonable, long hours can be a nuisance and make everyone less efficient and more prone to introducing bad ideas or bugs that waste time late.