When using a cold frame, one generally needs maximum sunlight and maximum heat, therefore south is the best direction. But keep iin mind, that it is usually 'cold' when using a cold frame, like in the 40's or 50's, or colder depending upon what crops are being grown.
If the cold frame is being used for some warmer weather purpose, then east facing, with shade to the west may be the better option. Also, on warm days, nearing 70 degrees or better, the cold frame must be opened, or the plants may cook. Some cold frames have an automatic opener.
Eclectic gardening style, drawing from 45 years of interest and experience. Mostly plant in raised beds and containers primarily using intensive gardening techniques.