Expensive trench coats or jumpers of the finest merino wool were not enough to protect investors from the cold wind that swept through luxury goods markets on Tuesday after Burberry issued a profit warning.Shares in the British fashion house plunged 22% after it said profits would be at the lower end of expectations this year.The firm is now taking steps to cut costs and maintain short-term profitability.Analysts warned Burberry's high-end rivals could be next, as fears over slowing demand, particularly in China, hit home.Shares in France's LVMH and PPR were both down 4%, while Swiss firm Richemont, which owns brands like Cartier and Mont Blanc, was down 5%.Prada, which is listed in Kong Kong, fell 4%, while in the US jeweller Tiffany & Co and Ralph Lauren were also both down.Broker Nomura, which downgraded Burberry to hold after the announcement, said the slowdown was a global phenomenon, primarily driven by lower traffic.Challenging conditionsBurberry, which has 196 retail stores, 207 concessions, 48 outlet shops and 58 franchise stores worldwide, said that trading conditions were becoming more challenging with like-for-like sales flat in the second quarter.The company, which had been riding on the crest of a retail wave driven by its popularity in the Far East, said retail sales growth at constant exchange rates was 6% in the 10 weeks to 8 September. Of this, new space contributed the whole 6%, while like-for-like store turnover was unchanged year-on-year, with sales slowing in recent weeks. Chief Executive Angela Ahrendts, said the second quarter retail sales growth had slowed against historically high comparatives. "Given this background, we are tightly managing discretionary costs and taking appropriate actions to protect short term profitability, while continuing to execute on our proven five key strategies," she said.Asian appetitesEven the economic powerhouse of China has been exhibiting worrying signs recently, with growth slowing more than expected.China, where demand for luxury Western goods had been very strong, reported falling imports and lacklustre growth in exports for August.Imports fell 2.6% from a year earlier, while exports rose 2.7% in August from a year ago.In July Burberry warned that it was seeing a slowdown in gift giving in China, including small leather goods, cashmere scarves, but also trench coats. At the time the firm put this down to the once-in-a-decade political change at the top of the ruling Communist Party making consumers nervous about spending.Whatever the cause, the slowdown in key Asian markets has helped take the sheen off a previously rampant Burberry.The company reported a 24% jump in annual profits to £366m in its last financial year, while total revenues were also up 24% to £1.9bn.DowngradeBroker Seymour Price downgraded Burberry to hold from buy until the firm released some better news on demand for its products."The trend Burberry is talking about may seem at odds with the rest of the sector news of late but we note that this is current news up until 8th September and would not be surprised if other luxury players are seeing similar trends," said analyst Kate Calvert.But she sounded an optimistic note, saying the slowdown was nothing like the brick wall the sector impacted in 2008 when the financial crisis hit. "Indeed, Burberry is in a much stronger position brand and infrastructure wise to react to a slowdown given recent system investment so is unlikely to have the same stock issues," Calvert said."We still consider Burberry a strong long term growth story with significant geographical and product mix opportunities."