While defining 1 Ton of Refrigeration (TR), why doesn't some specific value of pressure come into definition? Isn't freezing water (to ice) related to pressure? If yes then why do we go away with it while defining 1TR?
Very little, if at all for the range of pressures likely to be encountered in air-conditioning applications where the term is used. Water and ice are virtually incompressible so the pressure makes very little difference. (I am unable to find a good graph of this at the moment.) Steam, on the other hand, is compressible and the pressure affects the latent heat of evaporation.
Figure 1. Before mechanical refrigeration was invented, keeping something cool when it was warm outside was the job of ice. Ice would be collected during winter, transported to ice houses and stored until it could be sold for use in ice boxes. Image source: Forward Engineers.
Since ice was sold by weight and people had a concept of how much cooling a given weight would give it made sense to continue to use the "ton of refrigeration" measurement.
1 ton (refrigeration) = 3516.8 J/s (if spread out over 24 hours). That's 3.5 kW of cooling or 84 kWh. So at, say, 10 c/kWh that would cost 840 c per one ton ice cube.
For those not living in the colonies, 1 US ton = 907 kg. 1 tonne (1000 kg) would have a latent energy of fusion (if that's a valid term) of 92.6 kWh.