Even on cloudy days your solar light panel will be receiving a charge. This is because while the clouds do block the light, the sun is still shining and some light is getting through. It may not be as strong as on a clear day, but it is there.
There will be an impact, however, as weaker light means less power is added to your battery within your lights. The result will be reduced time that your solar lights operate. Even if your solar lights do not receive much charge during the day, you may find they still illuminate as power can remain in the battery for some time.