There has so far been light snowfall in several towns and villages, with the Met Office issuing a yellow warning for snow and ice for up until 6pm today.
It said: "Snowfall may cause tricky travel conditions in places. Some roads and railways likely to be affected with longer journey times by road, bus and train services.
"Probably some icy patches on some untreated roads, pavements and cycle paths." The Met Office also warned people to be careful to avoid slips and falls in icy areas.
Weather watching account Shropshire Weather added: "A cold and frosty start over Shropshire with plenty of sunshine. There'll be more cloud bubbling up in the afternoon and we could see some wintriness this evening."
There is currently just one flood alert in the county, at the Severn Vyrnwy confluence near Oswestry.
A statement on the Flood Warning Information Service website said: "River levels remain high but are falling at the Cae Howel river gauge. Flooding continues. We expect flooding to affect low lying land and roads adjacent to the river from the Welsh border at Llawnt to Shrawardine near Shrewsbury.
"Other locations that may be affected include Llanymynech, Maesbrook and Melverley.
"Further wintery showers are forecast over the weekend. We expect river levels to remain high until this evening. We are closely monitoring the situation. Please avoid using low lying footpaths and roads near local watercourses and avoid contact with flood water."
There have been no reports of train or road disruption caused by the weather so far.