It depends on the ice composition, amount, and where you release it
Current theory is that the previous ice ages were caused by large amounts of glacial ice being dumped into the Mid Atlantic Current, shutting it off sporadically and preventing the equatorial oceanic heat transfer to Europe and Canada (the main reason England is so rainy and warmer than its latitude should indicate is this effect).
Dumping a large amount of freshwater ice into the region occupied by the Mid Atlantic Current could replicate this effect.
link: http://www.sciencemag.org/news/2016/06/crippled-atlantic-currents-triggered-ice-age-climate-change
The time period would probably be shorter than normal, due the the same effects others have described, since we have too much heat trapping gas in the atmosphere.
Another interesting tidbit is that historically the southern hemisphere cools when the northern hemisphere gets warmer, and vice versa. Right now the ice sheets in Antarctica are actually growing (link: https://www.nasa.gov/feature/goddard/nasa-study-mass-gains-of-antarctic-ice-sheet-greater-than-losses) and this is one of the main talking points for global warming skeptics due to this historical pattern.
Edit: Wow this thread got necroed from last year, didn't even notice.