what kind of radiator is this? Can I build a wood cover for it?
It appears to be a "forced hot water" radiator, unless there is a steam vent you're not showing us. Also called "fin-tube radiators".  How the water is heated is not entirely relevant (oil, gas, wood, coal, electric, solar -- same radiator).  The fins conduct heat from the water in the supply pipes (tubes) and "amplify" the transfer to the air, which flows across the fins. Airflow may be natural convection or mechanically forced by a fan.  

You need to straighten the fins for best airflow (there are heavy-duty "combs" made for the purpose) and blow/vacuum them out from time to time, if you want to maintain maximum efficiency.  You can dress it in wood if you like.  They are generally designed to carry water no hotter than about 180 degrees F. Wood will not be as good at conducting or radiating heat as the metal enclosure. You must provide adequate air vents in any enclosure so that the warm air has a way to heat the room.

My fin-tube baseboards run nicely at around 150, except on the coldest days, at which point our on-site engineer raises the boiler temperature and chucks in more wood.