I would say the verse can be read on both levels, similar to the following verse:
Whoever works his land will have plenty of bread,
but he who follows worthless pursuits lacks sense.
Prov. 12:11, ESV
Somebody who puts effort into his land will have his reward, as the land will yield harvest. Similarly, if you take care of your animal, you will have your reward, since the animal will be healthy, provide food and multiply. This is also explained in verse 12 (the b-part):
Whoever is wicked covets the spoil of evildoers,
but the root of the righteous bears fruit.
Prov. 12:12, ESV
It is well possible that this series of proverbs has its origin in agricultural society and may be used in agricultural contexts. However, you may also use it in a more abstract context. Compare the English idiom "we reap what we sow": it can be used in a farmer context, but since most of us aren't farmers it is also frequently used in a more abstract context.
In that way, Prov. 12:10–12 can definitely be read more generally than regarding animal welfare / care of nature alone. Also consider that the verses explicitly refer to the reason for this treatment: you will "have plenty of bread" and "bear fruit". Thus, the reason for this treatment is not some intrinsic value of animals which animal right activists might advocate, but rather a cost-benefit analysis.