A yellow weather alert for wind is in place until 3pm on Wednesday for the Lothians and Borders and parts of northern England and Ireland.
The Met Office warned gusts of 40 to 50mph are expected widely, with some as high as 60 mph in some areas.
The warnings come just days after Storm Franklin and Storm Eunice brought snow storms, strong winds and heavy rainfall to the UK, causing widespread damage and power outages.
The blustery weather has forced Edinburgh Castle to keep its doors closed to visitors temporarily until staff have carried out appropriate safety checks.
In a statement, a spokesperson for the castle said: “Due to the current strong winds at the castle today, we are delaying opening until at least 1pm so we can carry out our safety checks.
“All ticket holders will be emailed with more info on when to use or how to re-book their tickets.
“For updates from the castle, please keep following us on our social media channels.”
Edinburgh’s Royal Botanic Gardens also closed its gates for the day, with a statement reading: “Due to high winds, the garden is closed today.
“We’ll be back open as soon as we can. Sorry for any inconvenience caused.”
Due to the high winds both Princes Street Gardens and Lauriston Castle will also remain closed for the rest of the day. Following safety inspections they will reopen on Thursday.
A separate yellow weather warning for snow and lightning is in place for most of Scotland from 5pm on Wednesday until 8pm the next day.
The regions affected include Central, Tayside and Fife, Lothian Borders, South West Scotland, Highlands and Eilean Siar and Strathclyde.
Weather experts said temperatures are expected to plummet overnight, with frequent heavy and blustery snow showers arriving from the Atlantic.
Snowfall of 3-7 cm is likely at low level, with 10-20 cm falling on higher ground by Thursday morning.
The snowy showers will be accompanied by strong, blustery winds, with a “small chance” of frequent lightning, which could impact power supplies, forecasters warned.