Know-how has a similar meaning to "smarts" in the context of "street smarts" - I'd say it better fits the type of practical knowledge and understanding that comes with country life (whereas "smarts" tend to be about instincts and reacting to fast changing situations). It also arguably sounds a little more traditional or folksy.
Then you just choose a prefix that is the appropriate contrast to "street" in "street smarts":
- country know-how
- farming know-how
- village know-how
For example, there's a book called Country Wisdom and Know-How, which seems to be about exactly what you describe:
Country Wisdom & Know-How is an unprecedented collection of information on nearly 200 individual topics of country and self-sustained living... including animals, cooking, crafts, gardening, health and well-being, and home
"City smarts" and "country know-how" have a nice ring together, for example:
Country know-how meets city smarts as Jim Mitchum and Ray Sharkey square off in TRACKDOWN (1976)
A few slightly narrower alternatives:
Country wisdom is also suggested (that book is based on "Storey Publishing's landmark series of "Country Wisdom Bulletins"). "Wisdom" has a similar meaning but suggests something more traditional, and more about understanding, while know-how is more about skills and abilities.
Country lore is a fairly common phrase, and gives across a sense of traditional rural knowledge inaccessible to outsiders; it's a good option for maximum contrast with "street smarts" because the implication is that country lore can only be passed down through the generations, while street smarts are learned on the streets. "Lore" meaning (from Google's definition):
a body of traditions and knowledge on a subject or held by a particular group, typically passed from person to person by word of mouth
- Bushcraft could work, but is specific to wilderness skills. It would cover things like making a fire and knowing which berries to eat, but wouldn't cover things like animal husbandry or village politics.