Often used figuratively for an entrance or opening, especially in phrases like 門戸を開く (open the door to) or 門戸を閉ざす (shut the door on).
The university is open to the community.
The country shut its doors to foreign companies.
The university opened its doors to international students.
The new regulations narrowed the door of opportunity for entrepreneurs.
ドア is the everyday word for a physical door, while 門戸 is more formal and usually used metaphorically for access or opportunity.
戸 refers to a traditional Japanese sliding door or shutter, whereas 門戸 refers more broadly to a gateway, often in a figurative sense of access.
open door policy
Compound of 門 (gate) and 戸 (door). The exact historical derivation is uncertain, but the combination has long been used to mean a door or entrance, both literal and figurative.
The government announced a policy to widen its doors to immigrants.
This field has come to open its doors to women as well.