If someone goes to Ft Drum N.Y., are they considered 10th Mountain Division?

No. There are multiple units at every base. Obviously some units are known for specific locations because they are bigger (such as division elements like 10th Mountain), but just being at a location doesn't mean that you will be in a particular unit (it doesn't mean you won't be either).

Only if they are part of the Division. There is non Divisional units at Drum, and it’s a possibility they may be assigned there.

As stated by others, no, not necessarily.
In addition, watch out for the requirements to earn your mountain tab. Unless tradition has changed, that is a hazing to avoid.

If you have orders there, good chance that your gaining unit will be a 10th Mtn unit. But, as stated by others, not everything at a post is part of a given division.

No. When I was there, there was only 3 Brigades at 10th Mountain that were considered "10th Mountain". While the rest are assigned there, I consider them 10th MTN. If you're looking for technicality on which units are and are not. I can't help you. There is an Air Force unit stationed there and I know for certain they are not 10th MTN.

Since you’re a 12b you will end up in 7th BEB most likely which falls under 1BCT 10th mtn

If you’re an Engineer, you will absolutely be 10th MTN DIV. First brigade has 7th Brigade Engineer Battalion, and Second brigade had 41st Engineer Battalion.

You might be there buddy. Like for example. I got orders to for Campbell. I’m in a beb(brigade engineer battalion) battalion and I’m still with the 101st AIR BORNE (AIR ASSAULT) division

Not unless they are assigned to the HQ or subordinate unit.

If you are active duty and stationed in fort drum to a u it there then yes you would be part of the 10th mountain Divison.