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The proper use of models or equations or both depends on what body of knowledge one is trying to discover. Austrian economists claim that the most fundamental body of knowledge about human action and interaction is the conceptual structure of human action and its logical implications. This body of knowledge can be acquired with a system of verbal logic. Within this “logic of action” thought experiments are used, such as the ceteris paribus stipulation you mention. One could call this a model, but it’s different than the models of neoclassical economics.
They claim that the most fundamental body of knowledge about human action are empirical regularities. It requires empirical-hypothesis testing to acquire this knowledge. The models used must be quantitatively definite, and hence their reliance on mathematics.
Austrian economists are skeptical of the possibility of discovering quantitatively definite empirical regularities in human action and interaction. It would seem, to the contrary, that the quantitative magnitude of the correlation between variables generated by human action is in constant flux. To paraphrase Ludwig von Mises, the problem is that there are no quantitative constants but only variables in the correlations among data sets generated by human action.
Austrians, then, would reject quantitatively precise, mathematical models but not reject verbally deduced, qualitative “models.” For example, Austrians would accept the “model” of demand and supply by which we can deduce that a larger demand for a good, with supply held constant, will result in a higher market-clearing price. Austrians would reject the model: D = a + bP and S = c + dP where a, b, and d are greater than 0 and b is less than 0 which results in a numeric magnitude for the market-clearing price determined by P = (a-c)/(d-b).