Is the following sentence proper grammar?
We tended to walk a lot. I think it should be We had a tendency to walk a lot, but I'm not sure.
It's proper grammar. "To tend" is a verb with several meanings, and one of those meanings is "to have a tendency". It is followed by the infinitive with "to". "Tended" is the simple past form of "to tend". The sentence is perfectly grammatical.
Your alternative is also perfectly grammatical, and also very good English. However, it is also long-winded and in some contexts may even sound a little pretentious. I prefer the original.