Hello Fabrizio,
Thank you for your message. Yes, the weather is particularly cold in the Andes this winter, so you must bring warm clothing (sweaters, anoraks or others, warm underware, long sleeved shirts, gloves, etc), specially for the evening. During the day it is very sunny but also cold. For the shoes, some trekkers use regular sneakers and others trekking shoes like the ones on the picture you sent us, it depends on their budget. If you can, trekking shoes are better because of the stone path.
For a complete list of what to bring, please check this page: http://www.inca-trail.com.pe/trek/recommandations.php?lg=en.
Should you need anything else, don't hesitate to contact us.
Best regards,