The headlights on my car are turning on at night by themselves on 2000 Toyota Corolla

I bought a new battery last week but apparently that's not the problem. It seems to only happen when it gets very cold outside. The light switch itself is not on but the headlights are and it drains my battwry every time ut does this! I need to get this fixed asap. Does it have something to do with the relay possibly? Any input would be greatly appreciated!! Ty in advance!!

Asked by for the 2000 Toyota Corolla
Do you think it's the daytime running lights circuit or the headlight circuit?
Not sure. Want to go buy whatever it is i need to fix it but dont know what the issue is thats causing it to do this? Not sure how to figure out what the exact issue is.
If you want to try, the Daytime Relay is in the right front of engine compartment, on the core support. You might remove it to see if it's in that circuit. The headlight circuit is more difficult to test out starting with the combination switch.
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