I'm in the US and have never heard the term "horse sense" used. If it originated in the United States, then it is not a commonly used term. I recommend only using "common sense" most of the time.

I have heard "horse sense" in the United States. I'm from the south and the phrase used most often is "he doesn't have the sense god gave a horse." Meaning he's stupid. I heard the term often when I was a child in Appalachia.

I'd agree. 'Horse sense' suggests a kind of practical good judgement, but it isn't a common or useful phrase for you to learn. Stick with 'common sense'.

I must admit that I had never heard the term 'horse sense' before I read your question, which suggests to me that 'horse sense' is a term used in the United States rather than in the UK. They mean exactly the same thing. Take care Naga

My grandfather who was born in the late 1800s told me as a very young man that "Horse Sense is the wherewithal that keeps you from getting yourself killed; Common Sense keeps you out of trouble."