well the problem would mainly be, the footprint and space a HID setup and the rest of your gear
heat can be fixed with a " HPS cool tube " type of reflector in a space that small (search around)

3 ft tall. take into consideration. the lamp will take up space, the pots & dirt will take up space
so that will leave you with about 1- 1.5 ft space vertical to grow.

T5 HO lamps have a small vertical foot print, 1-3 inches depending on the fixture
LED lamps also have a small vertical footprint
CFL lamps are bulky
HID lamps are also bulky

its all depends on your needs!

hope this helps!

-gd