Metal equipment and large plastic frames came off the lorry on the M4 near Chieveley.
The crash involved an HGV that came off the carriageway and ended up partially down an embankment.
Locations will be confirmed once feasibility studies are completed, says West Berkshire Council.
The horse was pictured behind a barrier on the M4, which was closed between junctions 12 and 13.
The collision occurred between J14 and J13 on the M4.
A group of MPs representing constituencies along the dual carriageway write to the government.
National Highways says the work will be rescheduled due to predicted adverse weather.
National Highways said a "long diversion" will be in place but will be the best route for drivers.
The crash happened on the M4 eastbound between Junction 12 for Theale and Junction 13 for Chieveley.
