At any instant in time the action and reaction forces are equal - but since as Sofia pointed out they act on different bodies, that doesn't mean they "cancel out": each of the bodies experiences one of the forces and accelerates accordingly. However, in a real world system it takes time for the "information" about the force to make its way through the entire object (this information travels at the speed of sound).
Because of this, the collision time between objects depends typically on their size and elasticity. This is closely related to the above - if you have a long rod that hits a wall, it takes time for the entire rod to even realize that it hit the wall, and the impact will last a long time (namely the time it takes for the shock wave to travel the length of the rod, reflect, and come back). This phenomenon is exploited in certain experiments to measure properties of materials - by hitting a small pellet of material with a long rod you can measure the force while the material experiences extremely high levels of strain for a (relatively) long time. This is described in detail in "Experimental methods at high rates of strain" by J.E.Field et al, Journal de Physique IV, Colloque C8, Supplément au Journal de Physique III, Volume 4, September 1994. Link: https://hal.inria.fr/file/index/docid/253331/filename/ajp-jp4199404C801.pdf
The mass and velocity of colliding objects plays very little role on the impact time $\delta t$ during an elastic collision although it can matter during an inelastic collision.