Many UK and Ireland flights have also been cancelled from London City Airport.
An airport spokesman said: "Bristol Airport remains open this morning but snow across Europe and the United Kingdom has caused disruption to a number of flights". Both Glasgow and Edinburgh are advising customers not to travel to the airport today.
Cork Airport remains closed and flights are not likely to resume until Saturday.
"Due to the Red Weather Alert for heavy snow all airlines have now suspended their flight operations to and from Dublin Airport for the remainder of today and tomorrow (Friday)".
Most of the United Kingdom remains under severe weather alerts, with two red, two yellow, and two amber covering most of Britain. As a result, it has introduced more flexible rebooking options for customers on shot-haul flights to or from London Heathrow and London Gatwick airports.
"Further snow is forecast during the day which will make travel conditions to and from the airport extremely challenging".
Your airline should get in contact with you to inform you that your flight has been delayed or cancelled.
The current status of flights can be seen here. It is keeping flights for later in the week under regular review.
At Edinburgh Airport, the majority of flights appear to be departing, however, there are flights to Shannon, Paris Charles de Gaulle and London Heathrow that are listed as cancelled on its website. Guests who have bookings to travel through March 2 can postpone their flight free of charge, with rebooked travel to take place within seven days of their original travel date.