This paper studies the existence and uniqueness of mild solution to stochastic Cahn-Hilliard equations, driven by fractional-colored noise, which is fractional in time and colored in space, with spatial kernel \mathrm{f}. A local solution is found by truncating drift term and applying variable substitution to stochastic integral. We prove the tightness of truncated solution by estimating Green function. Finally, a weak convergence of local solution is explored to verify the existence and uniqueness for mild solution of original equation. Coefficient conditions related to Hurst exponent H is then revealed. Furthermore, regularity of the skeleton are checked by applying Cauchy-Schwarz, Burkholder's inequalities and estimating Green function. It makes use of Gronwall's lemma and Girsanov's theorem to reduce large deviation form. We obtain Freidlin-Wentzell inequality in a special space, in which extension of Garsia's lemma plays an important role. The large deviation principle with a small perturbation can then be established.