Does anyone know what the weather is predicted to be towards the end of this year (late December/early January)? Also, during the day, would a sweatshirt or jacket suffice, or will I need to wear a coat? Thanks!

It depends on where you are going to travel in Spain. I've been to both Madrid and Barcelona at that time of year, and they were quite different. In Madrid it was pretty cold, especially when we went into the mountains to Segovia and El Escorial. I wore a winter coat, hat, scarf, and gloves nearly all the time. I think it actually snowed when we were at El Escorial that time, and I've been in Segovia previously when it has snowed, too. Since Barcelona is on the Mediterranean, it will be milder. The weather was lovely last December when I was there, but I think it was a bit of a heat wave. I had a wool winter coat, but I rarely needed my gloves, etc.

Spanish weather varies a lot depending on the place you are.
You can see the average climatological values ( valores climatológicos normales) city by city on the Instituto Nacional de Meteorología web page.
Click on "El tiempo"--> "Información climatológica" --> "Valores normales"

www.inm.es

Almería Airport:
Periodo: 1971-2000 Altitud (m): 20 Latitud: 36 50 35 Longitud: 2 23 17

MES T TM Tm R H DR DN DT DF DH DD I
ENE 12.5 16.9 8.2 23 69 3 0 0 1 0 7 191
DIC 13.7 17.9 9.4 23 70 3 0 0 1 0 6 176
AÑO 18.7 23.1 14.3 196 66 26 0 8 10 0 106 2965

Barcelona Airport:
Periodo: 1971-2000 Altitud (m): 6 Latitud: 41 17 49 Longitud: -2 04 39

MES T TM Tm R H DR DN DT DF DH DD I
ENE 8.9 13.4 4.4 41 73 5 0 0 1 2 9 149
DIC 10.0 14.3 5.7 51 73 5 0 1 1 1 7 138
AÑO 15.5 20.0 11.1 640 72 55 1 22 10 4 73 2524

Burgos City:
Periodo: 1971-2000 Altitud (m): 890 Latitud: 42 21 22 Longitud: 3 36 57

MES T TM Tm R H DR DN DT DF DH DD I
ENE 2.7 6.7 -1.2 46 85 8 5 0 8 20 4 90
DIC 3.9 7.6 0.3 57 85 9 3 0 6 16 3 74
AÑO 10.1 15.9 4.4 555 72 85 20 18 38 88 52 2183

Madrid Retiro Park:
Periodo: 1971-2000 Altitud (m): 667 Latitud: 40 24 40 Longitud: 3 40 41

MES T TM Tm R H DR DN DT DF DH DD I
ENE 6.1 9.7 2.6 37 71 6 1 0 5 6 8 148
DIC 7.0 10.1 3.8 56 74 7 1 0 6 4 7 124
AÑO 14.6 19.4 9.7 436 57 63 4 16 24 16 97 2769


T Temperatura media mensual/anual (°C)
TM Media mensual/anual de las temperaturas máximas diarias (°C)
Tm Media mensual/anual de las temperaturas mínimas diarias (°C)
R Precipitación mensual/anual media (mm)
H Humedad relativa media (%)
DR Número medio mensual/anual de dias de precipitación superior o igual a 1 mm
DN Número medio mensual/anual de dias de nieve
DT Número medio mensual/anual de dias de tormenta
DF Número medio mensual/anual de dias de niebla
DH Número medio mensual/anual de dias de helada
DD Número medio mensual/anual de dias despejados
I Número medio mensual/anual de horas de sol

Thanks for the help! Sorry I forgot to add that I'll be in Madrid. Looks like I will freeze.

Its gonna be in the 50's, but it can get pretty wondy so, take a coat!