1H NMR splitting of 3-methyl-1-butanol
In this example, HA is indeed split by HD, but you have quite rightly identified that we don't see coupling to the alcohol proton, HC. This is pretty normal that we don't observe couplings to protons that are termed labile; -OH, -NH2, -SH, for example. Whenever samples contain trace amounts of an acid or base, there will be very fast exchange between the alcohol proton and that other species (water is often the culprit). In solvents like chloroform (which this spectrum was run in), the exchange is very fast, and you just observe a single peak. In other solvents, such as dmso, you might observe two broadened peaks. But, the exchange means that any coupling to that nucleus is lost

We do sometimes observe coupling to alcohol protons. If you can eliminate exchange, or slow it sufficiently, you will observe 3J couplings as you would for any other nuclear coupling pathways. 3J couplings to alcohol protons are in the order of 3-6 Hz, commonly.