Sure, but its a bit harder to get around with a snowboard than it is with skis.
Basic snowboarding is discussed in the rec.skiing.snowboard FAQ.
There are three methods to carrying a snowboard up a hill that you plan to board. The first method is the least expensive in terms of gear. Use your hands.
Long leashing straps are also frequently used. This is easier than using your hands and not expensive, but its also uncomfortable. To make a leash, just get a long piece of medium width webbing and two adjustable buckles. Size it at home and cut off the excess webbing.
Finally, the most comfortable and most expensive option is to purchase a pack that can carry your board. Many manufacturers are offering packs that have an exterior pocket specifically designed for a board.
A recent addition to the spectrum of snowboarding equipment are split boards. A split board is a snowboard that has been cut into two separate pieces, and has a simple system that hooks the two pieces together. So for uphill travel, you use one piece of the board on each foot, and a pair of climbing skins (see Section 9.1). For downhill travel, the pieces of the board are attached to each other to create a full snowboard. The bindings on these boards have the ability to rotate so they are comfortable for both modes of travel. These boards are reasonably stong, but probably not strong enough for really big air, dOOd.
The most common way snowboarders climb a hill to board is to is simply to walk up in their boots by kicking steps in the snow. Should you choose this method, please do not walk in the skiers skin track.
Other options include lightweight snowshoes and cutoff skis with skins.