Yes, you can go out in the sun while taking beta blockers. But you should always protect yourself from the sun. Cover your skin and use sunscreen.
Less than 1% of people taking carvedilol have a reaction in the sun. Very rarely, in less than 0.01%, people taking metoprolol will have a reaction in the sun. Sunlight can cause a skin rash, itching, or sunburn. Contact your doctor if you notice any changes on your skin after starting beta blockers.
Block the rays for fun in the sun!