的样子 = seem like/ look like/ apparently
2月头的样子 (seems like early February) doesn't look like a complete sentence because we don't know 'what' seems like early February
If you wrote
"2月头的样子, (我会有一个长假)" --> It seems like early February, (I will have a long vacation time)
or rephrase it as
"It seems like I will have a long vacation time early February"
Then it would make more sense.
If you insist on just write "2月头的样子，有一起去泰国的朋友吗？" Then a topic must had been mentioned in the context earlier.
Q: "你什么时候去旅行？" ( When will you travel?)
A: "2月头的样子" (something like early February)
So it is similar (or same) to 左右?
Using 左右 (around) in this context would be fine, but the wording is different. As I stated in the beginning of this post, 的样子 means "seem like/ look like/ apparently"
"2月头左右, 有一起去泰国的朋友吗？" (Are there any friend who would go to Thailand with me around early February?)
It would be a complete sentence.