For a given alcohol the order of reactivity of halogen acids is:

As we know that atomic size increases from F to I, so bond length of H-X bond also gets increased and so bond dissociation energy decreases. Hence, ionization of H-X increases, therefore acidic strength increases in the order

HF < HCl < HBr < HI

So, the reactivity of alcohols towards halo acids is in the order

$\mathrm{HI}>\mathrm{HBr}>\mathrm{HCl}$