Brake & Battery idiot lights on, slow wipers

I started my car up last night and the brake and battery dash lights came on and have been on ever since. I thought it was odd that both lights came on and stayed on, and thought that maybe the same dashboard relay works both of these and now the relay was stuck. It's been in the single digits here and I thought that might have something to do with it. I'm thinking, I thought wrong. Electricaly everything seemed to be working fine until this morning when I put my windshield wipers on and they were pretty slow. So I'm thinking alternator maybe? Please help!

is your battery terminals fastened securely? check that out first. auto zone will test your battery, alternator if its any good for free. all you gotta do is bring it to them, off the car.

You can also test your alternator with a volt meter, look in your car's shop manual for what your charging voltage should be while the car is running (normally 14.something volts). Hook the voltmeter up to the battery and have someone hold the engine at 2,500 rpms.

Turn everything on that can be turned on (head lights, windshield wipers, heater's blower fan, A/C, etc.) and then press and hold the brake pedal, the voltage should stay at what ever is listed in the shop manual, if the voltage plummets into the low 13 to 12 volts range your alternator is most likely bad, have it tested.

I started my car up last night and the brake and battery dash lights came on and have been on ever since. I thought it was odd that both lights came on and stayed on, and thought that maybe the same dashboard relay works both of these and now the relay was stuck. It's been in the single digits here and I thought that might have something to do with it. I'm thinking, I thought wrong. Electricaly everything seemed to be working fine until this morning when I put my windshield wipers on and they were pretty slow. So I'm thinking alternator maybe? Please help!

This is the alternator. The brake and battery light both being on means this.