Does this Honda use a carburetor or is it fuel injected? I ask, because my 1990 Toyota p/u had a similar problem. A Toyota trucks forum explained the answer was due to the Auxillary Accelerator Pump leaking fuel. Since the AAP was operated only by vacuum and only when the engine was cold, the problem disappeared when the truck warmed up. The quick fix was to disconnect and cap both the AAP and the vaccum line that fed it. The permanent fix was to rebuild the carb. The kit came with all the parts for the AAP.
If it is fuel injected, you may want to look for a cold-start injector. If yours has one, and it leaks, this could also cause the problem.