Q: Was it dangerous? Is it according to standard procedure when approaching an airport in bad weather conditions?
If the aircraft did not go below the Decision Height, no, it was not dangerous and it was according to standard procedures.
Decision Height is defined as
DECISION ALTITUDE/DECISION HEIGHT [ICAO Annex 6] - A specified altitude or height (A/H) in the precision approach at which a missed approach must be initiated if the required visual reference to continue the approach has not been established.
[...] decision height (DH) is referenced to the threshold elevation.
The required visual reference means that section of the visual aids or of the approach area which should have been in view for sufficient time for the pilot to have made an assessment of the aircraft position and rate of change of position, in relation to the desired flight path.
DECISION HEIGHT- With respect to the operation of aircraft, means the height at which a decision must be made during an ILS, MLS, or PAR instrument approach to either continue the approach or to execute a missed approach.
This height is usually 200ft.
This means that when the aircraft arrives at the DH, the Pilot Flying (PF) must have decided whether to land or not. If an abort is initiated, he/she cannot modify the decision (as it would be unsafe)and a new decision has to be made during the new attempt.
If the pilot decided to attempt the landing, but conditions change later during the attempt, the pilot can still decide to abort (as in this case). The decision will be based on the current assestment of remaining available runway, aircraft speed, aircraft attitude and current engine throttle.
Q: What might have caused the pilot to actually land the second time but not the first?
The most likely cause is lack of visibility. In borderline conditions, a plane will normally follow an instrument approach down to decision height. At that height they look up, and if they see the runway clearly they land. If they don't they abort. The first time they didn't see it, and the second time they did.
In the general case, other conditions that might cause a go-around are:
- lack of preparation – “rushed” approach
- a late runway or approach procedure change
- an inadequate approach briefing
- challenging prevailing wind velocity
- inappropriate energy management
- inadequate traffic spacing
- unfamiliar approach - maybe a straight in non-precision or circling
- inappropriate aircraft configuration
- runway surface condition
- a predicted late touchdown point
- unexpected runway occupancy after clearance to land
- degraded aircraft systems status
- the effect of fatigue
- the effect of commercial and personal pressure (stress)
As for whether is common or not, I have no statistics at hand, but a go-around is definitely not unheard of. In the answer of Richard there is a statistic for a specific airport (Heathrow).