Conservation of momentum in a collision between particles can be understood from

We know that for a system, $F_{\mathrm{ext}} = \frac{dp}{dt}$

                                                  (from Newton's second law)

If F_ext = 0, dp = 0 $\Rightarrow$ p = constant

Hence, momentum of a system will remain conserved, if external force on the system is zero.

In case of collision between particles equal and opposite forces will act on individual particles by Newton's third law.

Hence, total force on the system will be zero.

Note  We should not confuse with system and individual
particles. As total force on the system of both particles is zero, but
force acts on individual particles.