They'll probably be OK, I rode the 50 miles that I've logged between Tring, the bivi and back on totally smooth-centre semi slicks at the weekend. Slippy in places but it really isn't bad out there currently. When it rains it's sloppy but currently it's still all draining fast (for here..), lots of leaf cover and the usual boggy sections are simply a bit soft at the moment. Real mud tyres would be less useful than an average tyre for me generally, there's a fair bit of harder-packed stuff, some of that is chalk and also leaves over roots.I only have summer tyres on my 29er
I would leave lighter Schwalbes at home, really

About timing, and eating -
If we aim to be rolling away from Berkhamsted by 10 that would be good but no stress. I can adapt the route to suit getting to Tring at 12. If arriving at Berkhamsted plan on doing 2hrs riding before we get to The Cog bike cafe in Tring for coffee and cake or hot food, it's about 2 miles after the Tring station stop.
We mentioned stopping at The Monument cafe in Ashridge, a good stop when it's quiet but can be rammed-busy and take ages to get anything and if we stop there we'll probably also need a stop for the Tring starters anyway.
The cafe in Wendover woods gets very busy on a nice day and if it's that kind of day a few of the trails close to the cafes are best avoided due to levels of dog-wires and kids :) So Tring town centre / The Cog looks like the best lunch spot for us. By the time we're at Wendover we'll be ~1.5-2hrs from the pub - there's plenty to ride near there or some could ride a nearby trail or two while others eat if we stop for say 45 mins. Then we can get the hip flasks out on top of Whiteleaf hill if there's spare time (nice viewpoint anyway) before dropping down to the pub about 5 mins away downhill.
The route I rode last Sunday (from Tring to the pub then to not far from Little Kimble then back to Tring, ie Sat and Sunday sections) in fair conditions on a semi-slicked 'gravel' bike was 50 or so miles (<2000m gain on the Garmin) and took a bit under 6 hours total, riding Sunday-steady rather than with any effort, if that's much use as a guide. It can be shortened quite easily as it's a weavy kind of route, or we can add miles on Sunday am. I thought we'd add a few hours to that time with food and faff and chat, loaded bikes also. On Sunday adapt the ride to Tring (via Crumbs Cafe in Wendover?) based on weather and what everyone wants to do. We could add a bit of 'Geoff Apps tribute' bushwhacking and mud-holing since we're in the birthplace of UK ATB riding..
https://clelandcycles.wordpress.com/rides/
I can't make it this year but should anyone want to join in it's a fun ride.