Even during a romantic walk in the Swiss Alps, Madonna makes sure she is heavily watched over by security. Our spies spotted Her Madjesty, 54, going for a snowy stroll in Gstaad with her dancer beau Brahim Zaibat, 24. But, according to our spy, “They weren’t exactly alone. They were shadowed by a huge SUV full of security guards, which crept along slowly behind them.” Madonna has also had extra protection on the slopes, where she is learning to ski. The source added, “She has a security guard and her instructor with her at all times, but the word is that when it comes to skiing, Madonna is human and keeps falling over.” The Queen of Pop is staying with design icon Valentino, who was last night due to throw a lavish bash at his chalet. Sources earlier told us that Madonna and “Les Misérables” star Anne Hathaway “are both expected to sing at the party and may even perform a duet.” Hathaway is with her new hubby, Adam Shulman, and local sources tell us the couple has been spotted canoodling in restaurants around town.