I have 2 questions regarding horsetail.

I've recently taken over an abandoned allotment. It's full of horsetail.
The person on the site next to mine said that my plot had been sprayed with
weedkiller sometime earlier this year. There are only a few horsetail
plants still showing green above ground, however, the soil is absolutely
chock-a-block full of horsetail roots, which are endless in length and more
or less impossible to dig out completely.

I'd like to take the lazy/easy/faster route and roto-till the plot, but I
know that horsetail will grow back from the tiniest piece of root.

My first question is: At this time of year, would live horsetail plants
still be showing green above ground?

My second question is: If the horsetail are dead down to the roots (fingers
crossed) can I presume that they won't re-grow from the thousands of pieces
of roto-tilled root?

Thanks.