We study uncoded transmission of a pair of correlated Gaussian sources over a two-user Gaussian broadcast channel (GBC) with perfect feedback links. Two linear coding schemes are considered: the Ozarow-Leung (OL) scheme and the coding scheme of Ardestanizadeh et al., which is based on linear quadratic Gaussian (LQG) optimal control theory. First, we derive an improved decoder for the LQG scheme which outperforms the original decoder in the finite horizon regime. Then, we bound the number of channel uses needed to achieve a certain distortion level for each of these schemes and show that in this finite horizon regime, the OL scheme can outperform the LQG scheme with either of the decoders. This is in contrast to the infinite horizon regime.