Hi my name is ***** ***** will assist with your query today.The setup is a perfectly acceptable solution providing the socket is covered by a RCD (residual current device) in addition to a standard circuit breaker, this will reduce the potential for electric shock, and critical for any outdoor appliances.
Assuming the socket is covered by an RCD (as it common for most electric installations),and your not getting nuisance trips, the only other thing to consider is the ingress of water and cold air through the hole the cable uses, but using some silicon around the hole would solve this.
Taking into account the assumptions around the RCD and that it doesnt pose a nuisance as is, I wouldnt have an outside socket fitted.
Should you require any further clarification please let me know.
Good evening my name is***** just wanted to check if you need anything else clarified.
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