Obviously Moz is in a different industry than cottage rentals, but one of the biggest things we heard about our redesign was that it was not responsive and did not render well on mobile devices. At least for our audience, they've come to expect that the site will be usable on something besides just their primary computer.
From the perspective of a small business owner though, I get you. I wouldn't imagine too many people are interested in ordering a USS Iowa hull from their phones, but I could be wrong. In your case, I would think it would depend on how far in advance people book your cottages. If there are some available with only a few days of notice, I would think having a site that works well for mobile would help when people are on a holiday and looking for their next place to stay.