Well, hot water does freeze faster than cold water. With a couple of contextual assumptions.
First, you have to let the hot water cool down to the same temperature as the cold water. From that point on, it WILL freeze faster, because the hot water was heated, and the heating process drove out dissolved air, leaving a different dissolved gas content (a lower one, often nearer to zero) which is what lets the "formerly hot" water freeze faster than plain cold tape water does.
Did that one in physics lab. Once you account for the assumptions, it is true.
On face value, as stated though, if you magically had 200F water and 50F water, the 50F water would normally freeze faster--even with the usual dissolved air.
A perfect case of "assumption" ruining perfectly good science.
If you would like to make the statement that water with different levels of dissolved gases freeze at different rates... I'm fine with that, but don't say that hot water freezes faster than cold water!
The hot water won't freezersooner than the cold water, but it will always freeze faster.
Faster refers to the rate at which freezing occurs, and as noted, since hot water has lost those pesky dissolved gasses while it was getting hot...it will be able to freeze at a faster rate.
You're confusing sooner with faster. Our marvelously imprecise English language.