Just reverse the door swing on the main door so you don't have to keep the door closed when working at your desk. And yes, remove the closet doors. I'd even look into built-in cabinetry for your desk and shelving above. Like this:

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Thank you! I was thinking of having a built in with floating shelves above.

It depends upon, during the life of the space, what you store in the closet and how much you want to conceal its tidiness or lack thereof.

I converted a closet to an office and kept the doors so I could hide my workspace. You do have to be careful when selecting your furniture so the doors can close.

Have the doors installed, then remove the hinge pins and store the doors in the garage, and use the closet as an office. If you have a messy office, install a curtain where the doors were.

If I were a betting man, I would bet the office desk will be moved within a year to some other place where daylight can be seen.

No curtain at all if you use the office as you mention you should have no mess and just get a jazzy office chair in a coolo color and a funky wall hung desk a small file box and be done no doors needed . If by chance this might be a bedroom on resale they can figure out the doors.

That’s what I was thinking. Make it super cute with a cool chair.

Definitely leave the closet doors off. I'm guessing there is no HVAC vent inside the closet and you would not want to be in there with the doors closed anyway.

How about doors like you used to see on an entertainment center; they slide back into a pocket on either side?

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I'm with @Mark Bischak, Architect. If you only work occasionally and can work in a space 6x3, why not place your desk under a window in another room? Traditionally called a writing desk, it's been done like this for quite some time.

Keep the closet doors and use the space to store office supplies and workout extras. I'm glad you planned plenty of storage because it fills up fast!

Is there even an outlet in the closet? Do you want to work while your husband is exercising? Will he have to knock just to enter in case you are in an online meeting?

If I had a desk in there it would not be in that small closet space. I would want a window or something pleasant but that is up to you.

I had a client from England that needed an office in the summer home I was designing with him. During the design process the office space moved around and changed size and shape. It ended up a little bigger than yours and not on the lake side of the house. It has a window in it opposite the appropriate door.

How about replacing your swinging double doors with a pocket door? You can leave open while working at your desk and close it when you are not or if things get kinda messy in there. Not absolutely sure it is possible but perhaps it could slide into the wall adjacent to the 3'-0"x8'-0" door into your study.

Make sure you have all the wiring you need and good lighting installed before the drywall gets completed.

thank you, I do have the wiring and lighting installed but can't add any walls at this point. We've been at this for almost a year and my husband would kill me if I delayed the progress, LOL.

Remove the doors and use a room divider between his exercise room and your work space.

Can you put the treadmill in the closet and the desk in the study?

I would swing the study door out into the hallway instead of inward, which will get in the way of the closet doors. I have a little desk area inside a closet in my bedroom and I love it. It keeps me convenient to the action in the house and I can shut the doors when I'm not using the space. Eventually, I'll take over our oldest son's bedroom once he's officially out of the house but this works for the time being.

That's a great idea. If I needed an office all the time I would use the study for it but just want a little nook available every now and then. Honestly I typically work on my laptop in my bed or on the couch, LOL.

NEVER EVER swing doors outward into the traffic pattern of hallway.

If you are talking 2 hours a week it doesn't matter. Leave the doors, lock the door to the room for those 2 hours, be done.

Since you have a study, consider how you could incorporate a small working area that meets your needs. I’d be happier in a congenial, spacious area vs a closet in a not so sweet smelling workout room lol.

The closet in workout room could actually be quite useful for equipment, keeping it off the floor, and even a mini fridge for water and fruit.

If you decide on the closet, perhaps a barn door would work.

By looking only at the partial plan provided, an outswinging door will not effect the traffic pattern of hallway any more than the inswinging door will.

I really like Jennifer's last layout.

I would not do doors at all. I would not want to feel confined in the office by the doors, or supporting wall stubs.

An outswinging door would be fine in this situation. However, a pocket door to the study would also work as well :)