I've had to reduce the height of a number of chairs (typically bar stools or countertop stools) so they fit.  On its own, it's difficult to get the cuts even height and co-planar with the floor.   I developed this technique.   I take some scrap wood and tack it together in a pattern like this (so there's no more cutting to size).   I used to carry a box of pieces of various heights and tack them together on site, big enough to fit around the largest leg.  Often the back legs are curved, so try them first.

Set up the chair on a flat surface and put the jig around one leg.   Saw 90% of the way through it with a trim saw held flush against the top of the jig.   Repeat for the other three legs.   Then complete the cuts free-hand.  Sand the sawn edges with a bit of roundover and color with a touch up marker (or stain).    Attach new or reused foot glides and you have a shorter chair that won't rock in the floor.

 

For reference, most dining chair seats are about 18" from the floor, plus or minus a bit.   But measure for your target environment being sure to allow ample thigh room below the aprons.

Thanks!

I am sooo tempted to shorten the Shop Foreman's stool.  To about 8 inches off the ground.  Now I know I can do a quality job.  

A great tip Keith, thanks!