Baxter was born on 26 December 1973 in Edinburgh, Scotland. He is the son of Iain and Sue Baxter, who were both British Ski Team members. Baxter's father named him after Alan Breck Stewart, a character from the Robert Louis Stevenson novel "Kidnapped", who was a rebellious Highlander. The French spelling led some to believe he was named after the 70s French skiing star Alain Penz. At 16 years of age, he was selected to the British Alpine Ski Team in 1991. Baxter's first 10 years of competition were achieved without him having access to any significant funding. Austrian journalists gave him the sobriquet "The Highlander". He steadily worked his way through the world rankings, making the top 100 in time for the 1998 Nagano Winter Olympics. At Nagano he straddled a gate and was disqualified, having been 15th-fastest at the checkpoint just before.