How to prevent TrigReduce auto evaluating Sin and Cos

There is one way:

    expr1 = Cos[2*t]^2 /. Cos[2 t]^2 :> Cos[(2 + x)*t]*Cos[2 t]

(*  Cos[2 t] Cos[t (2 + x)]   *)

Then

expr2 = TrigReduce@expr

(*   1/2 (Cos[2 t - t (2 + x)] + Cos[2 t + t (2 + x)])  *)

Now we can simplify the subexpressions under the Cos sighs, and replace tx by HoldForm[0] and x - by 0:

MapAt[Simplify, expr2, {{2, 1, 1}, {2, 2, 1}}] /. 
  t x -> HoldForm[0] /. x -> 0

yielding

I have no idea how your other terms look like. Therefore, I cannot garanty that it will work for the whole your complex expression. However, you can try to invent something along this line.

Please do not forget that HoldForm[0] cannot be operated by Mma functions. If you need to further operate with the result, apply first ReleaseHold.

Have fun!