The rail company also said emergency speed restrictions could be introduced and services might also be delayed due to icy conditions.
Transport for Wales (TfW) said from 15:00 on Friday the Craven Arms to Swansea service would be suspended.
There will also be a reduced timetable from 15:00 for TfW services between Cardiff and Crewe and on services from Shrewsbury to Holyhead, Aberystwyth, Crewe and Birmingham.
It said rail replacement services would not be able to run during the closures due to road conditions.
Shropshire Council said there would be no school transport on Friday or special education needs and disabilities (Send) school transport, even to schools which are open.
Many secondary schools in rural locations rely on coaches to bring in pupils from surrounding villages, and deliver them back at the end of the day.
Transport to adult day centres would also be suspended on Friday, the coulcil added, along with its Connect On-Demand service in Shrewsbury and surrounding villages.
Oldbury Wells School, Bridgnorth Endowed School, The Corbet School, Mary Webb School, Idsall School, Lacon Childe School, William Brookes School and Bishop’s Castle Community College are among the secondary schools to announce they will be shut on Friday.