Thats a great article, but he failed to mention two other points (one doesn't really apply to the UK and the other would put out a mixed message so probably why they're not mentioned).
As in the article, light to medium frosts freeze the cells of the plant so when they are walked on, the frozen water in the cell ruptures it, killing (or severely stunting the plant). However, my first additional point is when everything freezes up, it is less of an issue as everything is solid so the cells can’t rupture. It generally doesn't get that cold in the UK.
However, that leads to an issue when the weather is milder with, for example, warmer days and cold nights or after a rain event, the solid frozen soil will thaw at the top few inches. This results in the potential to sheer the roots off at the thawed/frozen interface when walked/driven on which undoes all the root growth from the fall and set the plant back as it has to regrow these roots for the following year as opposed to building onto healthy roots. It is a difficult decision to make when there are two days of 60F in February but a superintendent has to keep people off the course to prevent this.
Lastly is there was a bunch of Twitter posts over the last year - particularly from the UK - of greenkeepers mowing frozen turf and showing that it was ok afterwards. Like everything on the internet, blindly following it can be dangerous. Frost is not the same all the time. Depending on the temperature it can only freeze the leaf surface rather than freezing the whole plant, so the damage isn't as bad as you are not rupturing cells. I've seen frost that was nearly lifted leave tire tracks and heavy frosts, that didn't and everything in between. Since there is no practical way to know what its doing, its best to err on the side of caution and not damage the plant.
I'm not sure if this posted here in the past but this old pic (I can't remember who took it originally) shows the amount of steps one foursome takes on a green, which shows how much potential damage can be done, the plant is not thawed.
