I am not sure the software mentioned by Rasmus take vegetation into account. It depends on the methods implemented by the software. NoiseModelling is based on CNOSSOS-EU. This prediction model does not consider vegetation. SoundPLAN or CadnaA (https://www.datakustik.com/products/cadnaa/cadnaa) may offer several prediction models beside CNOSSOS-EU.
Depending on what you are looking for, vegetation may not be an issue at all, for instance when dealing with isolated trees or hedges and if what you want is the attenuation in dB. But if the bird sings in a forest and you want to study how the signal is distorted both in the frequency and the time domain as it propagates, then you really need to include the effect of foliage and/or tree trunks.
I can mention another open-source software named Code_TYMPAN (https://sourceforge.net/projects/code-tympan/) that implements at least one solver based on ISO 9613-2. The current version of the standard (1996) takes into account attenuation through a forest to some degree. But this does not mean that this specific feature is implemented in Code_TYMPAN. It may have been deemed unessential by the developers.
Since you mention temperature in the parameters of interest for you, this is certainly relevant for atmospheric attenuation in combination with humidity. But beyond a certain range meteorological effects may play a significant role. In that case, you would need the vertical temperature gradient and the occasional wind speed gradient as well.