Well I have some Dunlop gloves, they aren't massively thick but I can push the buttons very easily with them on. It only has the two big buttons on the front anyway. The right one cycles forward through the functions, the left cycles backwards through the functions. If you hold the left one down for a few seconds (for which it has a countdown indicator) then it resets the functions for the current journey to zero.
There is a button on the top but that is only used to edit parameters, (Manual entry of total KM, wheels size, time)
The ONLY thing I don't like about it is the rubber fastener that holds the bracket of the computer to the handlebar, I have a road bike with an oversized bar and it was a real stretch to get it on. I don't think its supposed to be stretched quite that far.
Hope this helps