Hi,
I am making a 2d game in which i want to implement a gun, which has the effect to make the character appear like frozen.

I am having doubt about how to show this effect. Do i have to keep a track to check what type of bullet is been used,
when hit by a frozen type, the animation shows that the character is freezing?

In order to implement it programmatically in Opengl and C++, how should i approach it.

All suggestions are welcome

I believe the word you are looking for is freezing not frozing which is not a word in the English language.

Now to solve your problem what you said basically summarizes what you need to do. You could easily shoot liquid out of the gun with particles, these particles would have some sort of ID that represents their value so that whatever touches them can be frozen. Now when your bullets "hit" the target you would slowly change that target from normal to frozen either using animation or some clever blending. Then if you wanted you could have the player "break" free by moving around. The faster they move the more the ice breaks which can also be done using animation. The code for this is pretty straight forward and I shouldn't have to explain it. I would start off with looking into animation and particle effects first though.

Hope this helps!
-Toaster