You have to pay attention to context. I’m thinking about cutting it. (Now) I was thinking about cutting it. (In the recent past. I’m still thinking about cutting it. The two sentences have the same meaning here, even though the tense is different) I thought about cutting it. (Grammatically correct but with a different meaning. In this case, you thought about it in the past and then decided not to cut it.)

The choice between "I was thinking about cutting it" and "I thought about cutting it" depends on the nuance you want to convey. "I was thinking about cutting it" suggests that the thinking was ongoing, perhaps over a period of time, and it might imply that the person was actively considering or contemplating the idea recently. It doesn't necessarily mean the thinking has stopped; it could still be a current consideration. On the other hand, "I thought about cutting it" is more neutral regarding the duration of the thinking. It simply means that the idea crossed your mind at some point in the past. It doesn't specify if it was a fleeting thought or if you contemplated it for an extended period. So, both phrases can be used to convey the idea of having considered cutting your hair, but the past continuous tense in the first example adds a sense of ongoing contemplation or recent consideration. If you want to convey that you had the idea about cutting your hair a couple of days ago, you could say, "I thought about cutting it two days ago."

Sure, you can say it either way. "I thought about cutting it" is a simple statement of fact. "I was thinking", on the other hand, creates an impression that he spent some actual time thinking. It creates an impression that the decision (whether or not to cut the hair) was an issue he considered for a while.