In ‘Yurp, where we have smaller and costlier everything, people are forced to use grass where there isn’t a blacktop airfield nearby courtesy WW2.
I don't know of anyone using grass with a Cozy Mk4, but I do know of one Cozy Classic which used to operate off grass, and the owner installed a larger nosewheel for this.
I have flown my LongEz off grass once, but it was a billiard smoooth grass runway.
Here’s a youtube video of Stefano Ferretti landing his VariEze on his Homebase grass runway in Italy.
Graham Singleton modified his LongEz to operate off grass by installing the nosegear 1” forward of plans location to encourage earlier rotation.
If you’re going to operate off grass, you have to know your own grass airfield intimately, and as others have said, watch out for rabbit holes, ruts, boggy patches etc. You have to have driven or walked it, talked to locals who know where the bumps are etc etc.
The other big disadvantage our aircraft have is the “pogo-stick” nose spring. That can get in phase with bumps and pitch you over. Stefano (in the above video) fitted a modified MTB damper to cope with this. I have made a few of my own versions and Ken McConnell (VariEze) has been testing it, and is very pleased with it. However, It only works with the manual retract mechanism.
So, grass might work if you set your aircraft up for it, if the grass was smooth, short, dry and well maintained (ie; like blacktop) but otherwise, keep to the black stuff.