Frost hardiness is the main factor affecting plant species distribution at high latitudes and altitudes. The main effects of freeze-thaw cycles on trees are damages to living cells, as well as the formation of gas embolism in xylem vessels, thus blocking sap flow in spring. The effect of frost on trees can be quantified through changes in branch diameter. In order to resorb embolism, some species (walnut, maple, birch, etc.) exhibit an increase in the xylem sap pressure during successive freeze-thaw cycles, which leads to the exudation of sap after pruning. The multiplicity of relevant scales (spatial and temporal), the presence of water simultaneously in gaseous, liquid and solid form, as well as the corresponding phase changes, bring complexity into the modelling of these phenomena. In this work, we present a numerical model coupling heat transfer, phase change, water and osmotic fluxes, taking into consideration different cell types within walnut branch tissues. We show how diameter and pressure variations are inter-related, and we validate the model against experimental results from the literature. We eventually show how this work can be adapted to other types of anatomical structures and to other environmental conditions, in order to explore inter-species differences.