I ski every year, normally stop in chalets but 2 years ago stopped in a swanky 4*/5* hotel and everyone still wore jeans for dinner. Apart from one lady who wore little black dresses and heels every night and stuck out like a sore thumb.
Never been there but have googled, Inghams go there and on their website it says dress code is casual. I'd put Inghams on a par with Mark Warner and people wear jeans in Mark Warner hotels for dinner. Think you'd be fine.