#Almost
Actually not quite. There isn't rules for building or maintaining roads, and certainly not which makes considerations for environment. D&D 5e trusts this kind of adjustments for your (the DM's) good sense.
That said you have some guidance to base yourself on. The Building A Stronghold section in the Dungeon Master's Guide (p. 128) includes some costs and construction times for things like towers (fortified; 15,000 gp), keeps (50,000 gp), or forts (15,000 gp).
You might be able to find more detailed descriptions for older editions or on the web, but they might not translate properly. Your own judgement is trusted, and I would personally advice that you set the cost to be substantial relative to their wealth; but then make particularly good use of the Hunting Lodge/settlement in your campaign going forwards.