We study fractional stochastic volatility models in which the volatility process is a positive continuous function σ of a continuous Gaussian process B. Forde and Zhang established a large deviation principle for the log-price process in such a model under the assumptions that the function σ is globally Hölder-continuous and the process B is fractional Brownian motion. In the present paper, we prove a similar small-noise large deviation principle under weaker restrictions on σ and B. We assume that σ satisfies a mild local regularity condition, while the process B is a Volterra type Gaussian process. Under an additional assumption of the self-similarity of the process B, we derive a large deviation principle in the small-time regime. As an application, we obtain asymptotic formulas for binary options, call and put pricing functions, and the implied volatility in certain mixed regimes.AMS 2010 Classification: 60F10, 60G15, 60G18, 60G22, 41A60, 91G20.