Looks like you have a hydronic boiler that is heating your house through multiple zones as well as heating your domestic water via a heat exchanger within the tank to the right. If so, this would be referred to as an indirect fired hot water heater.
During the warmer months, the boiler only needs to heat the domestic water as the zone control valves for the heating zones would be closed. This allows for 100% of the boiler’s output to be used to heat the water.
Now in the colder months, the boiler must satisfy all zones, including the domestic water tank. Therefore the output of the boiler is being shared to each of the zones as they call for heat and the zone feeding the water heater will no longer be getting 100% out the output of the boiler.
There could be many potential reasons that your’s is not keeping up with he demand such as:
- The boiler is undersized and cannot satisfy all the zones during peak demand
- Improper balancing of the zones
- Something piped incorrectly and causing a reduction in efficiency
A schematic diagram of your setup would be helpful in reviewing for potential issues. However, being that this seems to have always been the case, it might be that your boiler is undersized.
Regarding the addition of the a mixing valve and pump: where were they suggesting them being installed?
If you have turned up the tanks temperature too high, there is potential for scalding to occur at the plumbing fixtures. However it is often more efficient to run the water heater at a higher temperature and in these cases a mixing valve is installed on the outlet of the domestic hot leaving the tank to bring the temperature of the water as it leaves back to below scalding.
The only place I see that a pump might help would be on the heating zone that heats the domestic water tank. Similar to this setup:
However, a better understanding of your setup would be required to determine if feasible.