Hi there and thanks for your question.
Most dogs, chihuahuas included should be able to live just fine at 60 degrees. However, the dog should be able to indicate to you whether he or she is too cold. If you notice shivering or seeking heat (i.e. the heating vents, blankets, etc.) then you may want to either turn up the heat or get a jacket for him or her.
I hope this information helps! If you have more questions regarding this problem, just hit reply. If I am online I will respond right away. Otherwise I will respond as soon as I come online again. Or, if my answer is sufficient, then please hit accept. Thanks!
The above is given for information only. Although I am a licensed veterinarian, I cannot legally prescribe medicines or diagnose your pet's condition without performing a physical exam. If you have concerns about your pet I would highly advise contacting your regular veterinarian.