If $π : X → S$ is a family of complex projective
varieties, such that $X\_0 := π^{−1}(0)$ has simple normal singularities in $X$, then all the general fibers $X\_t$ have snc singularities at worst?



snc singularity is an open condition?
I am just posting my comment as an answer.


That is not correct. Already in projective $3$-space, cones over smooth plane cubics specialize to cones over unions of three lines, i.e., a simple normal crossings divisor consisting of union of three hyperplanes.


