Your husband’s reasons for not wanting tiles are unfounded.

I have tiles and not once have they become too hot. This would perhaps happen if you had dark shiny tiles, but who would??

You can buy outdoor tiles which are slip resistant as they have a slighy roughened texture for grip.

You can use the same tile in your kitchen as garden for continuity, just swapping for outdoor tile for the garden. It’s not even noticeable.
We have done tbis as it looks great, in summer when all doors are open it’s like once big space.

I recommend using bigger tiles, like slabs almost. You can get gorgeous porcelain tiles that look like natural stone now if you like this look.

A decking needs more maintenance as well.

I think I've probably got the "older grooved" wood decking referred to above but if I could have changed the decision I would have. It takes a bit of yearly maintenance (oiling/staining) that of course requires moving any furniture - and I like to cut down on compulsory maintenance where I can. 5 years on it's now rotted and broken so some of the boards have fallen through and I'm eyeing a replacement.

I'll probably go paving/stone/tile to try and avoid the need to replace it again so soon.

That said, some of the not-entirely-wood / plastic-like decking boards might have given me much better longevity.

I have both!  I have Ipe decking that looks a bit like the picture below, leading on to York stone.  To be honest, the decking is far more slippery when wet than the stone, which is grippy no matter the weather (well, apart from snow!!).  Neither the decking nor the york stone get too hot.

I agree that the old fashioned grooved decking is a bit cheap & cheerful, but you can get some really smart decking now - they also do a composite version of Ipe which you don't need to oil every year.

Jonny

We are just finishing a kitchen and I am keen to extend the floor out to the patio. My husband thinks that its not a good idea as he thinks stone would get very hot in the summer and very slippy in the winter and we are best to put wooden decking down for the patio. Would love some advice from anyone who has either and could share their thoughts. Thankyou.