I have to visualize flow over some designs in my wind tunnel. However, my advisor has stated that previous students have wrecked the machine when they have used oils and I think Dry Ice might interfere with the results owing to its different density and the fact that it will probably sink to the bottom of the tunnel (it is the horizontal kind).
In any normal wind tunnel, the wind speed will completely nullify the effects of thermal/density convection - unless you're testing some ultra-light apparatus that would work with airspeeds of order of 1m/s, just use dry ice - at ~5m/s airspeed the effects of density change and sinking rate will already be below threshold of other errors, and normally wind tunnel tests should involve airspeeds much higher.
I would recommend using an ultrasonic fogger/mister in a containor with distilled water. You would have to pump some air into the sealed containor with a diaphragm pump and then have a line running from the other side of that containor to the location in the wind tunnel where you need it. The shorter the distance the better, but the ultrasonic mister should sufficiently atomize it to travel without much loss. Once in the wind tunnel it will disappear quickly as the mist evaporates. I would recommend just increasing the quantity of mist to go a further distance. It wont create a mess, since you can control how far it travels before the mist evaporates.
If you want to go the dry ice route you could do it the same way, as the "smoke" you see is just condensed water vapor from the dry ice temperature. The CO2 will proprell the mist so you won't need the diaphragm pump. It will just cost more labor/money if your test is very long or frequent. It will also be much more difficult to regulate.
Also, I agree with SF. that the density difference will not likely affect your results. The amount of visualizing mist is very small compaired to the primary wind tunnel stream.