Thanks to artwork21 I could solve this like this:
IMap map = this._mapControl.ActiveView.FocusMap;
IEnvelope envelope = _mapControl.ActiveView.ScreenDisplay.DisplayTransformation.VisibleBounds;
IGeoFeatureLayer featLayer = myLayer as IGeoFeatureLayer;
if (featLayer != null)
{
IFeatureClass featureClass = featLayer.FeatureClass;
System.String shapeFieldName = featureClass.ShapeFieldName;
// Create a new spatial filter and use the new envelope as the geometry
ISpatialFilter spatialFilter = new SpatialFilterClass();
spatialFilter.Geometry = envelope;
spatialFilter.SpatialRel = esriSpatialRelEnum.esriSpatialRelEnvelopeIntersects;
spatialFilter.set_OutputSpatialReference(shapeFieldName, map.SpatialReference);
spatialFilter.GeometryField = shapeFieldName;
// Do the search
IFeatureCursor featureCursor = featureClass.Search(spatialFilter, false);
return featureCursor;