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We explicitly prove the horizon-entropy increase law for both causal andquasi-locally defined horizons in scalar-tensor and $f(R)$ gravity theories.Contrary to causal event horizons, future outer trapping horizons are notconformally invariant and we provide a modification of trapping horizons tocomplete the proof, using the idea of generalised entropy. This modificationmeans they are no longer foliated by marginally outer trapped surfaces butfixes the location of the horizon under a conformal transformation. We alsodiscuss the behaviour of horizons in "veiled" general relativity and show,using this new definition, how to locate cosmological horizons in flatMinkowski space with varying units, which is physically identified with aspatially flat FLRW spacetime.

The horizon-entropy increase law for causal and quasi-local horizons and conformal field redefinitions