Low voltage DC over long(ish) distance on a small cable
Power over Ethernet is the generic term for what you are describing. There is a widely adopted IEEE standard for the technology (IEEE802.3) and a thriving market for compatible equipment, although custom implementations are also used in some cases. The standard might allow you to do exactly what you want. Assuming you already need to run twisted pairs for data, you can also use the same cable for power. Type 2 (PoE+ or 802.3at) systems are designed for power levels up to 25W (the system voltage is about 50V).

You may not need some of the safety/handshaking/robustness features that an IEEE compliant solution provides, but you could take advantage of off-the-shelf equipment to get up and running quickly. You would want something marketed as a "PoE injector" where your mains are located and something sometimes called a "PoE splitter" on your load side. You can find these with a DC-DC converter built in that will provide 12V at your remote location. In the U.S., each of these can be found for less than $20. Make sure that the power level matches your needs (the 802.3af or "Type 1" only guarantees 12W at the load) and that it is compliant with your data standard (if you are diplexing the cable). 

That being said, you can certainly spin your own solution. The standard (and its market) have dealt with substantial challenges like supply inrush, cable surge, etc. that might cause you headaches along the way. Good luck either way!