I wouldn't trust a tenant to take care of the yard and wouldn't want to fight over what constituted care. That said, I have one tenant who works for a landcare company and yes I negotiated with him to knock down the rent and have him mow the lawn which he does at a blazing speed with his ZTR.
However, I DO make tenants responsible for snow removal because I talked to several plow companies who said it is a nightmare trying to deal with tenants having different schedules, not moving their cars, etc. The other reason I like this is that snow removal is a very unpredictable expense. Some years it could cost hundreds or thousands and other years almost nothing (because new england weather is crazy(.
As far as other repairs, I would not want to make those responsibility of the tenant. There have been many debates over this on BP, but my take is that as the owner I want to make sure things are fixed correctly. If I end up with a competent tenant and they make minor repairs on their own, then great! But it is hard enough to screen for a good tenant without trying to find one who is also a handyman or handywoman. Better to handle that myself or hire it out.