And are any current Mossbergs using them now?

The Mossbergs with Howa actions were called the 1500, 1550, and 1700.

No, Mossberg has not built their bolt action CF rifles around Howa 1500 actions for over 20 years. They switched to 3rd or 4th generation Raptor actions and continued to upgrade them.

I dont see many old Mossberg 1500s around but I dont think they are that difficult to find and probably not real expensive.

Smith and Wesson also badged that rifle.

PaulBarnard - found one of these (S&W 1500)in 1985 at a LGS. Came with a parkerized 24in heavy barrel and a hardwood stock for around $300. It did not set any records with factory stuff but sure liked Sierra 168gr MK's when I started hand-loading for it. Over the years picked up a few more HOWA's and they're a great rifle (and action) for the $$. Homesteader

I had one in 308. It was very accurate. It had nice wood as well.

You lucked out...my stock became dinged up by my ear muffs. No figured walnut here just plain vanilla hardwood. Changed it out several years later for a B&C VarTac stock with the aluminum bedding block and have not worried about it shifting POI since.
Homesteader

Sold one to a friend (S&W 1500) in Kodiak several years back in 223. He has repeatedly won their local shooting matches with it and routinely shoots clay pigeons at 500 plus yards with it.