Are 'out' and 'outside' interchangeable?

[MollyHuaCha]

To settle a disagreement, what are your views on the use of 'out' in this phrase:

"It's cold out, so I'll need a hat."

Acceptable? Or should 'out' definitely be 'outside' in this context?

Thanks

It’s fine colloquially, just in casual speech (maybe even preferable as it sounds less formal), but not in formal written English.

Thanks bluebiro :-)