I usually freeze my tissues on liquid nitrogen and storage them at -80°C until RNA extraction (according to the literature). I work with cardiac tissues but probably it might go well also with spleen. However you should be check some tissue specific information in the literature.
It all depends how long before extracting the RNA you will store the samples for. Short periods (a week or so) -80 deg should do, however, for longer periods I'd suggest N2(l) to avoid unnecessary degradation. It also depends on how much degradation your downstream experiments can tolerate. Either way, I'd go all the way and always give the "would-be" RNA sample the best preservation I could possible give. So, when I get samples I store tissue samples in lysis buffer + RNAseOUT (or similar) either at -80 (short-term) or N2(l) (long-term). If it is a chunk of spleen I'd suggest grinding the tissue when possible (as you would normally do) and store as advised above.
Using this approach I managed to keep tumour samples from FNA (Fine Needle Aspiration) and chunks for over 5 months, and when the RNA was extracted (using NucleoSpin RNA II) the RIN score (RNA INtegrity score) was ~7-8 for most of the samples, and passed the QC before RNAseq.
I think that -70°C (-80°C) is more than enough to prevent degradation. However, the most important step is RNA isolation. One should not melt sample before addition of homogenization buffer, or homogenize in liquid N2 after taking from -80°C. Good luck!
In case of short term storage (up to 6 months) you can store at - 80 , however if you are going to store for more than that , keep it dipped in LN2 , with keeping track on the level of nitrogen to be always above the tissue.
-70 is enough for long term storage but you need to add small step before you freeze the spleen tissue. I would suggest you to deep the spleen tissues in RNAlater by following the manufacturers protocol. This will allow you to preserve the spleen tissues in -70 for a long time subsequently from which very good quality RNA can be isolated. RNAlater preserves the RNA species inside the tissues in a very effective way and is well documented in scientific literature.