Augmented knowledge of plant responses upon application of stress could help improve our understanding of plant tolerance under abiotic stress conditions. Histone acetylation plays an important role in gene expression regulation during plant growth and development and in the response of plants to abiotic stress. The current study examines the level of transcripts and free metabolite content in transgenic Arabidopsis thaliana plants expressing a gene encoding histone acetyltransferase from Medicago truncatula (MtHAC1) after its heterologous expression. Stable transgenic plants with HAC1 gain and loss of function were constructed, and their T5 generation was used. Transgenic lines with HAC1-modified expression showed a deviation in root growth dynamics and leaf area compared to the wild-type control. Transcriptional profiles were evaluated after the application of salinity stress caused by 150 mM NaCl at four different time points (0, 24, 48, and 72 h) in treated and non-treated transgenic and control plants. The content and quantity of free metabolites—amino acids, mono- and dicarbohydrates, organic acids, and fatty acids—were assessed at time points 0 h and 72 h in treated and non-treated transgenic and control plants. The obtained transcript profiles of HAC1 in transgenic plants with modified expression and control were assessed after application of cold stress (low temperature, 4 °C).