Dogs like a lot of exercises.we often walk them in the park.

do exercise 做体操/做运动, 是固定搭配, exercise 是不可数名词, 没有复数的.

exercise 作"锻炼;练习"讲时,是可数名词. 前面有a lot of ,故用复数.

再如: I do special neck and shoulder exercises...
我做专门的颈部和肩部运动.
You'd better get up early to do exercise.
你最好早点起床锻炼身体.
再问： do morning exercises,和 I do special neck and shoulder exercises... 都是做可数句词讲喽
再答： do exercise 指泛指"做体操/做运动" 而具体做XX运动/或XX操, 就要用复数形式. 因此你说的这两个没错: do morning exercises,和 I do special neck and shoulder exercises... 都是做可数名词讲. 又如: We do eye exercises every day. 我们每天做眼保健操.