Some play is normal. The front wheels have a plastic hub bearing surface and the rear drive wheels have a steel insert bearing surface. The rear wheels should be serviced at least annually (cleaned/greased) along with the gears (drive and wheel). Nothing should be put in the fronts as the plastic is 'self-lubricating'. What happens is grit gets in them and can embed in the plastic, wearing the bearing surface of the axle bolt. Typically, the axle wears faster than the hub for that reason, so if you replace the wheels also replace the axles at the same time.
With the rear drive wheels, wear is not a problem until the wheel gets so loose that the gears don't mesh properly and drive is erratic.
Your mower is of the age now that if it has had normal use, it could be time for overhaul/service on the wheels/axles/gears.

Thanks for the reply - what would you advise in this scenario: the front wheels have 2 bushings each ( inner and outer ) , part number 27-6250. They are metal and pressed fit in each wheel. The rear wheels have the same set up. So would these wear more or would the shoulder bolt axle wear more -or both? Any thoughts?

It depends on the condition of the whole wheel assembly whether or not you would replace the bushings or just buy new wheels. I think you can drive the old bushings out from the other side respectively, because there is a space between them so that you can get the edge of a punch on the bushing and tap it out. You can probably tap the new ones in.
In my experience you would replace the axle bolts whether replacing the whole wheels or just the bushings. Otherwise you are likely to be disappointed with the results when the wheels are still wobbly. With this kind of bushing, you do clean and grease the front wheels as well as the rear. Make sure to fill up the space between the bushings with grease, which is one of the reasons its there.
Axle bolts are not expensive, so I imagine you can do the bushings and axles for about $20. A set of wheels would be about $80. You can measure the axle bolts and get them generically, but the factory ones probably have a black coating. I would get the Toro parts.

Thanks so much. Yes my wheels have a good amount of tread so I will give new axle bolts and bushings a try.

Just a follow up - I put new bushings and axle bolts in the front with grease and there is almost zero side to side movement in the wheels. Real nice. Thanks again.