We first review and analyze the Golden integral and its definitions and some properties. Then we introduce a new generalization of the Hermite polynomials via the Golden exponential function (called Fibonacci--Hermite polynomials) and investigate several properties and relations. We derive some explicit and implicit summation formulas for mentioned polynomials. Then, we analyze derivative properties and provide a higher-order difference equation of the Fibonacci--Hermite polynomials. Moreover, we examine a recurrence relation and integral representation. In addition, we obtain some properties of Fibonacci-Bernstein polynomials. Lastly, we obtain a correlation between the Fibonacci--Hermite polynomials and the Fibonacci--Bernstein polynomials.