Heat loss in the water is the most common form of risk. If your variety of fish need warmer temperatures you can wrap their container in a blanket and be sure it is set away from drafts that might cool it. Even on cold days, the sun may shine and its rays will penetrate windows, gradually warming everything they meet.
Cold weather is more damaging to marine and saltwater fish and other aquatic life.
Most of these require water temperatures in the upper 70's, and any significant drop in temperature could be fatal. Many of these need 12-18 hours of light, especially coral reef setups. If you are very concerned over these pets, purchasing a small gas or diesel generator will help. Generators put off toxic fumes, so keep them outside where they have adequate ventilation. Keep a long, weather-proof extension cord handy, so in the event of a power failure, you can run it from the generator inside.