Lattice gauge theories are lattice approximations of the Yang-Mills theory in physics. The abelian lattice Higgs model is one of the simplest examples of a lattice gauge theory interacting with an external field. The most important observables in lattice gauge theories are Wilson loops. In several recent works, the leading order term of the expected value of Wilson loops was calculated in the low-temperature regime, both in the absence and in the presence of a Higgs field. In the absence of a Higgs field, the Wilson loops are important observables since they exhibit a phase transition interpreted as distinguishing between regions with and without quark confinement. However, in the presence of a Higgs field, this is no longer the case, and a more relevant family of observables are so-called open Wilson lines. In this talk, we will describe the abelian lattice Higgs model's basic features and present a recent result on the leading order term for Wilson line observables.