Scotrail said services on the Stranraer line between Girvan and Ayr were disrupted by a tree on the tracks, with Network Rail sending a chainsaw team to the site.
There have been snow gate closures on the A93 and A939 roads, while the southbound A1 was restricted at Eyemouth due to a fallen tree.
CalMac has warned of possible disruptions to ferry sailings on the west coast.
Ferry operators Stena Line and P&O also cancelled their crossings between Cairnryan and Northern Ireland on Saturday in light of the forecast.
Meanwhile, the Energy Networks Association reported 86,000 homes in England, Scotland and Wales were without power.
‘Nasty conditions’
Met Office presenter Clare Nasir told the BBC’s Good Morning Scotland programme that winds on the east coast could peak at around 60mph on Saturday evening.
She said: “It will make for some very nasty conditions this afternoon.”
Transport Scotland said road, rail, air and ferry services were likely to be affected with longer journey times and cancellations possible.
Its resilience room and multi-agency response team will both be activated to monitor conditions.
Transport Secretary Fiona Hyslop said travellers should “plan their journey in advance, drive to the conditions and follow Police Scotland travel advice”.
Ch Supt Hilary Sloan, head of road policing, said: “Drivers of vehicles vulnerable to being blown over should plan their route to avoid exposed areas, or consider delaying your journey until conditions improve.
“Plan ahead and keep updated by checking the Met Office and Traffic Scotland websites and social media.”
Police travel advice to drivers in the area affected by the amber warning is to consider if they really need to travel or if it could be delayed until conditions improve.
Flood duty manager David Morgan said: “There’s a risk of surface water and river flooding in central, southern and north-eastern areas due to persistent, and at times heavy, rainfall.
“People living, working and travelling in affected areas are advised to consider any steps they need to take now to be prepared and stay safe.”