Economics of Barn Roofs
Pole barns refer primarily to the exterior wall construction method. Poles are structural members set into the ground; they support the roof of the barn and walls, if walls are used. A pole barn can employ any conceivable kind of roof, though it probably doesn't make sense. A pole barn is an economic means of basic shelter. It calls for an economical roof.
Common Pole Barn Roofs
Most pole barns are constructed with a simple, low-pitched roof. There are no hips or anything complex about them, just a single ridge-line with unceremonious gables at either end. Construction methods of this design vary. It may be framed, trussed, or timber-framed with purlins. However, there are few reasons the roof needs to have a ridge-line and two pitches, opposed to a single flat roof (parallel to the ground) or a single-pitch "shed roof."
Shed Roofs
A shed roof can be employed on a pole barn where the pitch of the roof only runs in one direction. It is a flat roof, with no gables or ridge-line, though it is not parallel to the ground or parallel to "level" if it is built on a slope. Like all roofs, if a shed roof is employed, it must have an adequate pitch and strength to handle the maximum snowload possible in the area. The longer the span, and the higher the potential snowload, the steeper the pitch requirement. Shed roofs with open-walled pole barns open one unique characteristic: wind. If the high end of the roof isn't covered in a curtain wall or some kind of siding to block wind, the roof becomes wing-like. If wind approaches the structure from the "open" side of the barn, it can create significant lift instead of down force or sheer force. It must be engineered for the wind contingency.
Flat Roofs
Flat, level roofs are probably not the most economic choice for a pole building for this simple reason. To provide for the maximum potential snowload, a flat, level roof requires stronger structural members. That's basic physics. A sloped roof deflects weight, so it doesn't require as much strength. If your design calls for a flat roof it can be accomplished by timber framing members and purlins, or flat trusses, such as scissor trusses.