I am installing drywall in the bedrooms of a seasonal cottage in northern Ontario. It is unheated in the winter. The cottage is insulated with R14 insulation. Will the installation of a vapour barrier behind the drywall cause mold issues?
Presumably you are going to have heat early/late in the season, when it gets cold at night. If you ever want to heat the cottage in the winter, it's also significantly easier to do now than it is later.
I would install a vapour barrier in this case. It's needed when warm meets cold; in cold climates, on the warm side, to prevent moisture from forming condensation in the insulation. It also helps prevent air flow (drafts) which can otherwise make insulation fairly ineffective. You should have a continuous seal around the building, meaning the vapour barrier should be taped and sealed with acoustic caulk.
Buildingscience.com has some great articles on this, I highly suggest you check it out. For example, this speaks to the purpose and how different wall constructions work: http://www.buildingscience.com/documents/reports/rr-0412-insulations-sheathings-and-vapor-retarders/