Cold fronts are a primary feature of the day-to-day variability of weather in the midlatitudes, and feature in conceptual extratropical cyclone models alongside the dry intrusion airstream. Here the climatological frequency and spatial distribution of the co-occurrence of these two features are quantified, and the differences in cold front characteristics (intensity, size, and precipitation) when a dry intrusion is present or not are calculated. Fronts are objectively identified in the ECMWF ERA-Interim dataset for the winter seasons in each hemisphere and split into three sub-types: central fronts (within a cyclone area); trailing fronts (outwith the cyclone area but connected to a central front); and isolated fronts (not connected to a cyclone). These are then associated with dry intrusions identified using Lagrangian trajectory analysis. Trailing fronts are most likely to be associated with a DI in both hemispheres, and this occurs more frequently in the western parts of the major storm track regions. Isolated fronts are linked to DIs more frequently on the eastern ends of the storm tracks, and in the subtropics. All front types, when co-occurring with a DI, are stronger in terms of their temperature gradient, are much larger in area, and typically have higher average precipitation. Therefore, climatologically the link with DIs increases the impact of cold fronts. There are some differences in the statistics of the precipitation for trailing and isolated fronts that are further investigated in Part II of this study from the front-centred perspective.