I've driven several different hondas and several different makes of cars over the years and in cold weather I've noticed a slight ticking (that increases with engine rpm) until the motor warmed up on almost all of them. On some cars it's all the time in cold weather (until the engine warms up) while on some it does it some times and not others. I've always heard that this is normal. I know from experience (with a '90 prelude) that using thicker/heavier oil does increase the ticking noise, in that case it was oil much thicker than recommended and the result was a much louder ticking, clacking from the cam lobes and lifters I'm assuming.
My current car, '92 Civic EX, doesn't seem to do this noticeably unless it's quite cold but according to the manual it is normal to hear a slight ticking or knocking(not sure of exact wording) while holding a constant speed, even when warmed up. It says this is a sign the engine is running at it's most economical. I've noticed this a few times but it's very quiet and not very noticeable.

I'm FAR from an expert but it seems possible that if the valves or the timing needed adjusting it could increase those noises (or cause them to begin on a quieter motor).