The airport tweeted: "All flights are currently suspended until 0800 whilst our teams work to clear the runway and other operational areas.
"Please refer to your airline for specific flight information."
Disruption has also been reported to the Air Decker bus service which runs to the airport.
At shortly before 11pm last night Bristol Airport commented: “Flights are currently suspended so snow can be cleared from the runway, taxiways and aircraft stands.
“Passengers are advised to contact their airline for flight information.”
The airport started giving customers the updated information, warning flight would be suspended until 8am, shortly