Answer
No, see explanations.
Work Step by Step
Step 1. Given $y=x-cot(x)$, we have $y'=1+csc^2x$
Step 2. For a horizontal tangent, let $y'=0$; we have $csc^2(x)=-1$.
Step 3. As there is no solution to the equation above, we can not find a horizontal tangent.
