How do I update my ugly mobile home closet doors?

Try peel and stick wall paper or hang curtains in front of them

You could add moldings to them.

Maybe replace them with a different type of door? Barn doors are great. Or paint them?

Bi fold or sliding doors? If they are sliding just paint them and you could add decals for some unique and eye catching decor ideas.

https://www.amazon.com/s?k=wall+decals&i=garden&ref=nb_sb_noss_1

Definitely some paint! I love the look of dark gray doors right now! But white would also update them and make them look fresh. I would use a paint specifically for doors and trim and use a really good bonding primer before the paint.

You can use thin pieces of wood and add them to look like they are higher end doors. Shaker style, farm style etc.

Take a look here for some ideas:

https://www.pinterest.com/adnillrig/closet-door-redo/

Sliders are great in mobile homes. They give you more usable floor space. I'd stay away from folding as I think they take away from any look. There are also sliders that actually slide into the wall, instead of 1 side behind the other. I'm not sure if that is a possibility in your mobile home. You don't say square footage, single, double or what rooms. The theme & size of each room makes all the difference.

Or you could replace them with double doors. Just getting rid of the sliders will update the look.

Paint them or change handles or add Trim.

Paint and add panels using trim or plastic panels. You can make them look like 6 panel doors.