Just had the same thing happen on my V70. It was the check valves in the washer system. When they fail, the fluid squirts out the bottom of the valve instead of going through the lines to the headlights / windshield.

The check valves for the windshield are under the hood, just beneath the fluid nozzles. If I recall, there are two ... one is a "T" connector on the right side, and the other an "L" elbow on the left side. If it takes more than one minute each to change each of them you're doing something wrong. I think the replacments were about $3 each.

The one for the headlights is located underneath the right headlight housing. Open the hood and look down under the right headlight ... you will see one larger hose going to the valve and two smaller ones coming off the valve. This area is a little tight to work in, so be patient and don't tear the hoses while removing the old valve ... there isn't that much slack to begin with. The replacment valve here was $4.

Interestingly enough, the new valves do not have a hole in the bottom. Perhaps Volvo had a better design that evolved along the way?

Happy squirting!