It seems that tertiary alcohol is more reactive than other alcohols. This is because of the presence of an increased number of alkyl groups, which increase the +I effect in the alcohol. Additionally, the reactivity of primary and secondary alcohols are lower as they contain fewer alkyl groups, so they are less positive and therefore don't increase the positive charge of the carbocation as much.
Overall, I believe it would be safe to suggest that tertiary alcohols have greater reactivity with hydrogen halides than secondary alcohols, which in turn have greater reactivity than primary alcohols, in reactions forming alkyl halides.
I hope this helps!