Should I vent my kitchen range vertically or horizontally?
It shouldn't be a problem to vent the range hood out the wall, just make sure you check your local codes before doing so.  I wouldn't think this would be a problem, but there could be different laws in densely populated areas as apposed to rural regions.  And laws/codes can vary depending on your locale.

Make sure you install the vent properly, and include a back flow prevention device (unless you like cold/warm air coming in from outside).