Your cold water comes directly from the main line without hitting resistance. Your hot water travels through your water heater which may decrease the pressure. Is this a new problem or has it always been like this? If it is a new problem you may be getting build-up in the lines near the water heater or even in the water heater.
Hot water also tends to have more deposits in the piping. If you have galvanized piping, you could have a lot of corrosion in the pipes. Hot water heaters do get scaling build up. It might be worth having it checked out, a broken hot water heater can be pretty messy!
The answer may differ according to where you live. In the UK the cold water comes from the main which is kept at a moderately high pressure, for example by a water tower. Any leaks are then "outwards" with less chance of inward contamination. The hot water in a house is generally provided from a tank in the house attic, which auto-refills when water is drawn off, stoppnig when full by a floating arm which cuts off the supply to it. This tank at relatively low height provides lower pressure water to the house boiler.
Don't you think the new water pressure valve regulator may have caused this/ did the plumber install smaller piping? Look for it could also be a slight problem with air in the line
My guess is that the hot water heater is installed downstream from a pressure reducer to limit the maximum water pressure that the water heater is exposed to.
Water pressure increases as the water gets warmer. If water is cold, it doesn't provide much pressure because the molecules move slowly.
low/poor water pressure coming from the utilities/street
The water pressure when one turns on the hot water is lacking because the water is coming from one's water heater, which is at the same level as the faucet, whereas the pressure from the cold valve is coming directly from one's town's water tower, which is at a much greater elevation. Also, the water heater tank is only a few feet high, whereas the water holding cell in a water tower is several feet high. The potential energy of the water tower far exceeds that of one's hot water heater, thus the cold water flows out of the faucet with much more pressure.
These are the five feelings 1. Hot 2. Cold 3. Pressure 4. Touch 5. Pain
Pressure is the same whether hot or cold.
The piping has to be the exact same length for each shower head from the tee where the cold and hot water feeds from the top of the diverter faucet.
Install on cold water line.
More than likely it is restiction in your water heater.
If you mean to ask if cold bodies of water are associated with high or low atmospheric pressure, they aren't. Atmospheric pressure can change independently of the temperature of bodies of water.
Hot or cold?
It is so cold.
water pressure
Low water pressure or cold water main undersized.
The cold side inlet may be plugged with sand or rust.
My guess is that the hot water heater is installed downstream from a pressure reducer to limit the maximum water pressure that the water heater is exposed to.
It depends on the pressure. At normal atmospheric pressure, the melting point of water is about 273.15 K.