I understand your worry as a concerned mother. The baby being cold
to touch is not a good sign. However, her back is warm. Please check if her extremities are pinkish or bluish in color.
If she is able to feed normally on your breast, if she is not crying excessively, if she is breathing normally, and if her extremities are pink then there is absolutely nothing to worry at all.
If in doubt, it is always better to get her examined by her pediatrician
rather than making assumptions.
As for now, I feel your daughter is normal.
I wish her good health.