I ride year round down to near freezing temps and have the same issue but it only last for about a mile and then my eyes seem to get used to it as long as I'm not going really fast, like a steep descent, when they tend to tear up no matter what the temperature.

If you haven't already, you might try just starting out at a very leisurely pace till your eyes adjust to the cold and then transition to your normal speed.

If it's a sustained issue about all you can do is get better wind protection, i.e. enclosed goggles or large shield.