I have white smoke coming out from the front cylinder. It is light and I guess more noticeable when warm.
The pistons and rings are new, as well as the valves were just done.
However, I was running very rich for quite a while (about 3k miles) and managed to foul several plugs, mostly in this front cylinder.
Could it be just accumulated carbon still burning out?
How can I tell if it is oil or not (not enough smoke to tell how it smells)?

The plug looks ok now, on the white side, but still a bit darker than the back cylinder one. But I guess it would be also the case if it is just an exhaust valve seal leaking...

 

It can be several things from a leaking valve seal, to a poor fitment on the valve to guide, a cylinder that is washed out from the overly rich state of tune. Also a oil ring that has a problem. You can have great compression and leak down and still have oil controls problems from your oil ring.
A bore scope to look into the cylinder is very helpful. Price has come way down and can save many hours of time in some cases. Maybe a shop close to you can help you out with that??

 

Once you, or a shop pulls it down, then the evidence will surface.
It will not get better.