What type of reaction feels cold to the touch?
A endothermic reaction.
Endothermic reactions are those that must absorb energy from their surroundings. This can include absorbing heat from the container they are in, or from your fingertips. The result is that both the container and your fingers will feel cold.
It is also possible, if the reaction occurs in a thermally insulated container, that the kinetic energy of the molecules will be reduced to increase the potential energy of the system. Lower kinetic energy means lower temperature. Hence, it cools.