I've been onto Microsoft Surface support. They had no useful suggestion apart from using theprintspace.co.uk but its prices are horrendous. Surely lots of users want to make prints of their photos. If only I could Winzip them and send them to my old computer.
Do you have a wireless network at home? Is your printer connected to the wireless network?
If not, can it be connected to the network?
If not, get a new printer.
If so, you should be able to just send them to the printer with no problem.
Lacking that, you could always use the sneakernet. Stick a thumb drive in the USB port of the Surface, copy the pictures to the thumb drive, then put the thumb drive in your desktop ( or directly in your printer if it supports that ) and print from your desktop.