In general, most dogs don't mix too well with cold weather. There are, of course, a few exceptions....some dogs who enjoy cold climates, but on average, dogs don't like the cold, especially Chihuahuas. Chihuahuas are very much warm weather dogs, and very much dislike the cold.
At this time of year, it's important to remember your dogs when you're trying to keep warm. A no brainer....if temperatures are approaching freezing, your dog should not be left outside. At the very least, he should have access to shelter out of the elements, preferably with a blanket or something to curl up with, where he can more efficiently use his own body heat to keep warm. Ideally, he should be indoors in a heated environment. If your dog is in a structure which does not have central heat, be careful using space heaters. Please be sure that you keep them on a non-combustible surface, such as cement, and that you keep them away from any fabric, paper, etc., to prevent fires. Also, be careful that your dog cannot come into contact with the heaters, as they can be very badly burned should they brush against them.
Cold weather can have many effects on your dog's health. As with humans, exposure to cold temperatures, especially for prolonged periods of time, degrades the immune system and opens your dog up to illness. Cold weather also stiffens joints, leaving your dog more likely to develop arthritis. It slows the digestive process and reduces your dog's energy level, which leads to weight gain. Tiny paws can freeze very quickly, resulting in frostbite that may not end well for your or your dog. Taking your dog out side for a short time to get some exercise is fine....necessary in fact. But please don't leave him out. Let him exercise and then bring him back inside to keep warm.
Note: Chihuahuas and other small breeds should NEVER be left outside for longer than a few minutes during the winter months. They are much more susceptible to the cold than larger dogs are, and excessive shivering, coupled with exposure to the elements, can make tiny dogs sick very quickly. These small dogs need a heated environment. Simply keeping them out of the elements is not enough for them. Please be sure that you house your small dogs inside your home during the winter!