Tree ferns cover a large amount of possible ferns, most of whom are not that hardy. The hardiest is Dicksonia antarctica. The fronds on those are hardy till -3C and the growing point until -5/-8C depending on location and overhead cover. Unless there is sustained freezing for days then there is no need to fleece a Dicksonia...an old blanket is all that is really needed to cover the growth point.
Given that the current mild weather is forecast to stay until at least the end of next week, I would not cut off green fronds for the sake of some uninformed commentators on an online forum. Straw only works by getting it thick enough to rot down and thus release heat. It also attracts vermin and pests to the growing point. It would be better to make a cage using chicken wire and stuffing that with straw. I would only do that if 2010 type of weather was forecast as it is overkill.
It is crucial to keep the tree fern damp all year round. More die of drying out than cold weather.