My problems with harvesting wood in the spring is not about the sap being "down"; there are ways around that. Water rushes into any tree in the spring, so, yes the wood is wet, and that can give you trouble drying without checking, etc, but slow drying, reducing and then drying, etc.. have proven to solve the checking, warping, and getting eaten by bugs/fungus problems.
The trouble I have had in the spring is with white woods, especially if fine grained. Even thin ringed wood will make a bow if it has good density, but if you have a spring growth ring on the back in stand of a nice solid, smooth summer wood ring, that back is just not very strong in tension. Even worse is when you have a PART of a summer ring, eggshell thin, over a porous winter/spring ring. I've actually had elm and ash start to crack on 5he back, but not really break, just life up chunks and flakes, because they can't take the tension.
So, if you cut spring wood, dry it carefully and chase/scrape down to a thick, established summer ring for your back.