You are probably fine. Many vegetarians actually have more balanced diets than those that eat meat. The fact that you eat eggs and drink dairy products makes your diet even more complete. The ability to maintain body heat is something that we only very rarely lose, and this only comes in some extreme circumstances. The apparent temperature of your skin does not always represent what your core body temperature is. Your skin temperature will change depending on whether your body is trying to release or keep heat. Take your oral temperature some day and make sure it is somewhere between 97-99 degrees (core temperature). The causes of inability to maintain body heat are thyroid problems (low thyroid hormone), deficiencies in thiamine (also known as vitamin B12, severe infections (such as sepsis), and a few other causes. It would be quite unlikely for you to have a deficiency in something that would cause hypothermia without some other major symptom.
Because you are a vegetarian, it is probably not a bad idea for you to periodically get some vitamin levels checked. This can be done by your primary care physician
or internal medicine doctor
). In addition, your doctor can prescribe you any vitamin supplements that you need. Good luck.