If you stay inside a lot and don't go out when it's nice then you won't get the needed Vitamins from the sun which keeps you healthy so it's not very healthy to always stay inside the house and never venture out much.
But on really cold days it's really best to stay inside the house or somewhere warm since that would be better for your health.
But when you're cooped up in the house you're breathing in allergens and any viruses that may be around in the house so even if it's cold you should step outside the house for at least a few minutes each day.
On nice days as long as you step outside a few times per week you should be okay.
I sometimes stay in the house for 4 to 5 days at a time without leaving the house but do step outside and go somewhere at least a few times per week.