No, it is not safe to use your cordless drill outside in a drizzle. Do not expose power tools to rain or wet conditions. Water entering a power tool increases the risk of electric shock. This applies to cordless tools because their internal electronics and battery terminals are not sealed against moisture.
If you must work in a damp location, use a Ground Fault Circuit Interrupter (GFCI) protected supply. For a cordless tool, however, the safest action is to wait for dry conditions. Using the tool in the wet can also lead to premature battery cell failure.
Store the tool and battery pack in a dry location. Do not store them where temperatures can exceed 105°F (40°C), such as in a metal shed in summer.