There are NO assumptions in any linear model about the distribution of the independent variables. Yes, you only get meaningful parameter estimates from nominal (unordered categories) or numerical (continuous or discrete) independent variables. But no, the model makes no assumptions about them. They do not need to be normally distributed or continuous.
It is useful, however, to understand the distribution of predictor variables to find influential outliers or concentrated values. A highly skewed independent variable may be made more symmetric with a transformation.