Context. Substructures in stellar haloes are a strong prediction of galaxy formation models in ΛCDM. Cold streams, e.g. from small satellite galaxies, are extremely difficult to detect and kinematically characterize. The COld STream finder Algorithm (COSTA), is a novel algorithm to find streams in the phase space of planetary nebulae (PNe) and globular cluster (GCs) populations. COSTA isolates groups of (N) particles with small velocity dispersion (between 10 km s −1 and ∼ 120 km s −1 ), using an iterative (n) sigma-clipping over a defined number of (k) neighbor particles. Aims. We have applied COSTA to a catalog of PNe and GCs from the Fornax Cluster VLT Spectroscopic Survey (FVSS), within ∼200 kpc from the cluster core, to detect cold substructures and characterize their kinematics (mean velocity and velocity dispersion). Methods. We have selected more than 2000 PNe and GCs from the FVSS catalogs and we have adopted a series of optimized set-up of the COSTA parameters, based on Montecarlo simulations of the PN and GC populations, to search for realistic stream candidates. We have found 13 cold substructures, with velocity dispersion ranging from ∼ 20 to ∼ 100 kms −1 , which are likely associated either to large galaxies or to ultra-compact dwarf (UCD) galaxies in the Fornax core. Results. These streams show a clear correlation of their luminosity with the internal velocity dispersion, and their surface brightness with size and distance from the cluster center that are compatible with dissipative processes producing them. However, we cannot exclude that some of these substructures have formed by violent relaxation of massive satellites finally merged into the central galaxy. Among these substructures we have: 1) a stream connecting NGC 1387 to the central galaxy, NGC 1399, previously reported in literature; 2) a new giant stream produced by the interaction of NGC 1382 with NGC 1380 and (possibly) NGC 1381; 3) a series of streams kinematically connected to nearby ultra compact dwarf galaxies (UCDs); 4) clumps of tracers with no clear kinematical association to close cluster members. Conclusions. We show evidence for a variety of cold substructure predicted in simulations. Most of the streams are kinematically connected to UCDs, supporting the scenario that they can be remnants of disrupted dwarf systems. However we also show the presence of long coherent sub-structures connecting cluster members and isolated clumps of tracers possibly left behind by their parent systems before these merged into the central galaxy. Unfortunately, the estimated low-surface brightness of these streams does not allow us to find their signatures in the current imaging data and deeper observations are needed to confirm them.