An indirect exciton is a bound pair of an electron and a hole confined in spatially separated semiconductor layers. Long lifetimes of indirect excitons allow them to cool down to low temperatures below the temperature of quantum degeneracy. This gives an opportunity to study cold exciton gases. We will present spontaneous coherence and condensation, phase singularities, spatial ordering, and polarization textures in a cold excitons gas in the presence of an external magnetic field. We develop a theoretical model accounting for the spin-orbit interaction of electrons and holes, exchange splitting of exciton states and Zeeman effect. This model reproduces the main features of polarization textures observed experimentally and confirms that the polarization textures at low temperature manifest ballistic propagation of cold excitons over the distances exceeding the exciton Bohr radius by 3 orders of magnitude and the exciton thermal De Broglie wavelength by more than an order of magnitude.